Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello,

Please , how can we plot two figures with different X-axis and the same Y-axis ?

Thank you

 


 

restart

``

Lambda := proc (z) options operator, arrow; int((z-u)*phi(u), u = 0 .. z) end proc

proc (z) options operator, arrow; int((z-u)*phi(u), u = 0 .. z) end proc

(1)

k := diff(Lambda(z), z)

int(phi(u), u = 0 .. z)

(2)

k

int(phi(u), u = 0 .. z)

(3)

m := subs(phi(z) = 1/2, k)

int(phi(u), u = 0 .. z)

(4)

``

``


 

Download dummy2.mw

Hi,

 

I'm trying to learn the dsolve command on Maple. I have a second order differential equation and two initial conditions to solve it.

I'm following maple help's procedure to solve it. But in the end i don't get my constants solved (which i do if i use Matlab i.e.)

What am i doing wrong?

restart;
ode := diff(Y(y), y, y) = 3*(1-(y/b)^2)*q/(4*k*b);
                                    /     2\  
                                    |    y |  
                                  3 |1 - --| q
                                    |     2|  
                  d  / d      \     \    b /  
                 --- |--- Y(y)| = ------------
                  dy \ dy     /      4 k b    
dsolve(ode);
                         2       4                
                    3 q y     q y                 
             Y(y) = ------ - ------- + _C1 y + _C2
                    8 b k        3                
                             16 b  k              
ics := Y(b) = Ts-Tb; (D(Y))(-b) = 0;
                         Y(b) = Ts - Tb
                          D(Y)(-b) = 0
dsolve({ics, ode});
                      2       4          
                 3 q y     q y           
          Y(y) = ------ - ------- + _C1 y
                 8 b k        3          
                          16 b  k        

               16 _C1 b k + 16 Tb k - 16 Ts k + 5 b q
             - --------------------------------------
                                16 k                 

or a screenshot:

 

 

 

 

I have a package that uses fsolve, a Maple function known (to me) to often fail when UseHardwareFloats is set to true. Since I set UseHardwareFloats:=true in my .mapleinit (for I want hardware performance when using floats) I set UseHardwareFloats:=deduced; in the ModuleLoad routine of this package. ModuleLoad executes as evidenced by a print statement in the routine that does in fact print, and within ModuleLoad, UseHardwareFloats is set to deduced. But at the worksheet level, UseHardwareFloats remains set to true.
 The only way I can set it is to set it explicitly in the sheet that calls the package. I tried various things, like putting it into the body of the module, using :-UseHardwareFloats, and so on. Nothing seems to work. While not a fatal issue it is bothersome & has had me run around with code not working several times.

Any hint would be appreciated.

Mac Dude

 

 

Maple can solve the easiest two problems of the Putnam Mathematical Competition 2018.  link

 

 

Problem A1

 

Find all ordered pairs (a,b) of positive integers for which  1/a + 1/b = 3/2018

 

eq:= 1/a + 1/b = 3/2018;

1/a+1/b = 3/2018

(1)

isolve(%);

{a = 1358114, b = 673}

(2)

# Unfortunalely Maple fails to find all the solutions; eq must be simplified first!

(lhs-rhs)(eq);

1/a+1/b-3/2018

(3)

numer(%);

-3*a*b+2018*a+2018*b

(4)

s:=isolve(%);

{a = -678048, b = 672}, {a = 0, b = 0}, {a = 672, b = -678048}, {a = 673, b = 1358114}, {a = 674, b = 340033}, {a = 1009, b = 2018}, {a = 2018, b = 1009}, {a = 340033, b = 674}, {a = 1358114, b = 673}

(5)

remove(u ->(eval(a,u)<=0 or eval(b,u)<=0),[s]);

[{a = 673, b = 1358114}, {a = 674, b = 340033}, {a = 1009, b = 2018}, {a = 2018, b = 1009}, {a = 340033, b = 674}, {a = 1358114, b = 673}]

(6)

# Now it's OK.

 

Problem B1

 

Consider the set of  vectors  P = { < a, b> :  0 ≤ a ≤ 2, 0 ≤ b ≤ 100, a, b in Z}.
Find all v in P such that the set P \ {v} can be partitioned into two sets of equal size and equal sum.

 

n:=100:
P:= [seq(seq([a,b],a=0..2), b=0..n)]:

k:=nops(P): s:=add(P):
numsols:=0:

for i to k do
  v:=P[i]; sv:=s-v;
  if irem(sv[1],2)=1 or irem(sv[2],2)=1 then next fi;
  cond:=simplify(add( x[j]*~P[j],j=1..k))-sv/2;
  try
    sol:=[];
    sol:=Optimization:-Minimize
         (0, {x[i]=0, (cond=~0)[], add(x[i],i=1..k)=(k-1)/2 }, assume=binary);
    catch:
  end try:
  if sol<>[] then numsols:=numsols+1;
     print(v='P'[i], select(j -> (eval(x[j],sol[2])=1), {seq(1..k)})) fi;
od:
'numsols'=numsols;

[1, 0] = P[2], {5, 10, 13, 14, 16, 19, 21, 23, 24, 26, 28, 31, 32, 35, 36, 38, 40, 41, 43, 46, 47, 49, 52, 53, 55, 57, 59, 62, 64, 67, 69, 70, 73, 75, 76, 79, 81, 82, 85, 86, 88, 90, 92, 93, 94, 95, 97, 98, 99, 100, 102, 103, 106, 107, 109, 112, 113, 115, 118, 120, 121, 126, 128, 135, 138, 144, 150, 154, 159, 165, 168, 170, 171, 172, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 219, 222, 225, 228, 229, 230, 231, 235, 236, 237, 238, 240, 241, 242, 243, 246, 248, 252, 253, 254, 258, 260, 261, 264, 266, 267, 270, 273, 274, 275, 276, 279, 280, 284, 287}

 

[1, 2] = P[8], {3, 7, 10, 13, 14, 16, 19, 21, 22, 25, 27, 28, 31, 32, 34, 36, 37, 40, 42, 44, 46, 48, 50, 52, 55, 58, 59, 61, 62, 64, 66, 69, 70, 73, 74, 76, 77, 81, 83, 85, 87, 88, 91, 93, 94, 97, 98, 100, 102, 104, 106, 108, 110, 112, 115, 117, 118, 121, 122, 124, 126, 132, 135, 139, 140, 141, 144, 151, 153, 159, 171, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 220, 222, 223, 225, 229, 230, 231, 234, 236, 237, 238, 240, 241, 242, 243, 246, 249, 250, 252, 255, 257, 258, 259, 261, 263, 266, 267, 269, 273, 276, 279, 281, 282, 284}

 

[1, 4] = P[14], {7, 10, 13, 15, 19, 21, 22, 24, 26, 28, 31, 32, 33, 37, 38, 40, 42, 44, 47, 48, 50, 52, 55, 56, 59, 60, 63, 64, 66, 68, 71, 72, 75, 76, 78, 81, 82, 87, 88, 90, 91, 94, 95, 96, 97, 100, 102, 103, 105, 106, 109, 110, 113, 114, 115, 116, 117, 118, 121, 122, 124, 127, 132, 135, 138, 142, 144, 145, 154, 156, 159, 160, 163, 165, 170, 171, 172, 176, 177, 178, 179, 180, 181, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 216, 219, 220, 222, 225, 226, 228, 229, 231, 232, 234, 235, 237, 239, 240, 241, 244, 245, 247, 248, 250, 251, 253, 254, 255, 258, 261, 262, 264, 265, 267, 268, 270, 272, 273, 276, 284}

 

[1, 6] = P[20], {10, 14, 15, 16, 19, 22, 24, 26, 28, 30, 31, 34, 35, 37, 40, 43, 44, 46, 47, 51, 52, 54, 56, 58, 60, 62, 65, 66, 68, 70, 73, 75, 76, 79, 82, 83, 84, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 102, 103, 106, 107, 109, 110, 114, 116, 117, 120, 121, 123, 126, 127, 128, 129, 130, 135, 138, 142, 144, 147, 152, 153, 154, 156, 157, 162, 163, 172, 174, 177, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 223, 224, 225, 226, 228, 229, 233, 234, 235, 236, 237, 241, 242, 246, 248, 249, 250, 251, 252, 253, 255, 258, 259, 262, 263, 265, 267, 269, 270, 273, 275, 276}

 

[1, 8] = P[26], {4, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 29, 30, 34, 36, 37, 38, 40, 43, 44, 46, 48, 51, 54, 55, 56, 58, 61, 63, 64, 66, 70, 71, 73, 74, 78, 79, 80, 82, 85, 86, 88, 90, 92, 94, 97, 100, 102, 103, 106, 108, 109, 112, 113, 115, 118, 120, 121, 123, 129, 133, 135, 141, 144, 150, 158, 159, 160, 163, 168, 169, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 219, 220, 222, 225, 226, 228, 230, 231, 232, 233, 234, 237, 240, 241, 243, 245, 246, 249, 250, 255, 257, 258, 259, 260, 261, 262, 264, 265, 267, 269, 270, 273, 279, 281, 282}

 

[1, 10] = P[32], {3, 4, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 37, 38, 40, 43, 44, 46, 49, 51, 52, 54, 58, 61, 63, 64, 65, 67, 68, 70, 73, 74, 78, 79, 81, 82, 85, 86, 88, 91, 94, 96, 97, 100, 103, 104, 106, 108, 109, 112, 113, 115, 117, 119, 121, 126, 131, 132, 136, 138, 144, 147, 148, 153, 156, 160, 161, 168, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 219, 220, 222, 224, 225, 226, 227, 228, 231, 233, 234, 236, 240, 242, 243, 245, 246, 248, 249, 251, 252, 254, 255, 257, 258, 261, 262, 264, 266, 267, 269, 270, 273, 275, 276, 279, 282}

 

[1, 12] = P[38], {7, 10, 14, 16, 19, 22, 25, 28, 29, 31, 34, 35, 36, 37, 40, 43, 46, 47, 48, 49, 52, 54, 57, 59, 61, 63, 64, 67, 68, 70, 72, 75, 76, 79, 81, 82, 85, 87, 88, 90, 93, 94, 96, 98, 99, 100, 101, 103, 106, 108, 109, 111, 112, 114, 117, 118, 121, 122, 124, 132, 135, 141, 150, 151, 158, 159, 162, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 221, 222, 223, 224, 225, 228, 229, 230, 231, 232, 234, 235, 237, 239, 240, 243, 244, 246, 249, 250, 251, 252, 255, 258, 259, 260, 261, 264, 267, 270, 273}

 

[1, 14] = P[44], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 49, 51, 52, 54, 57, 58, 61, 62, 64, 65, 69, 71, 72, 73, 76, 78, 80, 81, 84, 85, 88, 90, 93, 94, 95, 100, 102, 103, 106, 109, 111, 112, 113, 115, 117, 120, 121, 124, 127, 132, 133, 138, 141, 145, 150, 153, 159, 162, 165, 168, 171, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 234, 235, 236, 238, 241, 242, 243, 244, 247, 248, 249, 252, 256, 258, 259, 260, 261, 264, 267, 268, 270, 272, 273, 275, 276}

 

[1, 16] = P[50], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 53, 54, 56, 58, 61, 63, 64, 67, 68, 70, 72, 74, 76, 78, 82, 84, 85, 87, 88, 90, 92, 94, 96, 99, 103, 104, 106, 107, 109, 111, 115, 116, 118, 121, 123, 127, 132, 138, 141, 143, 147, 156, 159, 160, 168, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 222, 225, 226, 227, 228, 231, 232, 233, 235, 238, 240, 242, 243, 244, 246, 247, 249, 250, 252, 253, 255, 256, 258, 259, 260, 261, 264, 267, 270, 272, 273, 275, 276, 281}

 

[1, 18] = P[56], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 60, 62, 64, 66, 68, 70, 73, 75, 76, 78, 80, 82, 85, 86, 88, 89, 93, 94, 96, 98, 100, 102, 105, 106, 109, 110, 113, 114, 116, 118, 119, 121, 123, 129, 132, 136, 144, 148, 153, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 217, 218, 219, 221, 222, 223, 225, 229, 230, 234, 235, 237, 239, 240, 243, 244, 245, 246, 249, 250, 251, 252, 254, 255, 256, 257, 258, 259, 260, 261, 263, 264, 266, 267, 269, 270, 273, 276, 279}

 

[1, 20] = P[62], {3, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 63, 64, 67, 68, 72, 73, 74, 76, 79, 80, 81, 82, 85, 87, 88, 90, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 114, 116, 117, 120, 121, 126, 127, 132, 135, 141, 147, 153, 155, 163, 169, 172, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 228, 229, 232, 234, 235, 237, 238, 240, 243, 244, 246, 248, 249, 253, 254, 255, 258, 261, 262, 264, 267, 268, 270, 273, 274, 275, 276, 279, 282}

 

[1, 22] = P[68], {12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 73, 74, 75, 76, 78, 79, 82, 83, 84, 85, 88, 90, 91, 93, 94, 96, 98, 100, 103, 104, 109, 111, 112, 114, 115, 117, 119, 121, 124, 129, 132, 136, 138, 141, 142, 150, 153, 156, 159, 160, 168, 169, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 216, 217, 218, 219, 220, 224, 225, 226, 228, 230, 231, 232, 233, 237, 238, 240, 241, 243, 247, 249, 251, 252, 253, 254, 255, 258, 261, 262, 264, 267, 270, 273, 274, 275, 276, 279, 282}

 

[1, 24] = P[74], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 78, 79, 81, 82, 85, 87, 88, 90, 92, 94, 97, 99, 102, 105, 106, 109, 111, 112, 113, 115, 117, 120, 122, 126, 127, 129, 132, 133, 138, 139, 144, 147, 153, 160, 165, 166, 168, 169, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 225, 227, 228, 229, 230, 231, 232, 233, 234, 237, 239, 240, 244, 245, 246, 247, 249, 251, 252, 253, 255, 258, 261, 262, 264, 267, 270, 273, 275, 276, 277}

 

[1, 26] = P[80], {3, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 82, 83, 84, 86, 88, 91, 92, 95, 96, 99, 100, 103, 104, 106, 108, 110, 112, 115, 117, 120, 121, 124, 125, 126, 127, 128, 130, 132, 138, 139, 141, 145, 150, 153, 159, 162, 166, 174, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 221, 222, 223, 225, 226, 228, 229, 231, 233, 234, 235, 236, 237, 240, 242, 243, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 268, 270, 273, 274, 275, 276, 279, 282}

 

[1, 28] = P[86], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 90, 91, 92, 94, 97, 98, 101, 102, 104, 106, 109, 111, 112, 115, 116, 119, 120, 123, 124, 129, 132, 134, 136, 141, 147, 153, 160, 162, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 224, 226, 227, 228, 233, 234, 236, 237, 240, 241, 243, 244, 245, 246, 247, 249, 250, 251, 252, 254, 255, 257, 258, 259, 260, 261, 263, 264, 266, 267, 270, 273, 276, 279}

 

[1, 30] = P[92], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 93, 94, 97, 98, 100, 103, 105, 107, 108, 109, 110, 111, 113, 115, 117, 119, 120, 121, 122, 123, 126, 127, 132, 135, 141, 147, 153, 157, 165, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 225, 226, 228, 229, 231, 234, 235, 236, 237, 240, 241, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 268, 270, 273, 275, 276, 279, 281}

 

[1, 32] = P[98], {10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 102, 105, 106, 110, 111, 112, 113, 114, 118, 120, 121, 123, 124, 126, 127, 128, 129, 130, 135, 138, 144, 150, 153, 156, 157, 160, 162, 166, 167, 171, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 217, 219, 221, 222, 223, 225, 227, 228, 229, 232, 233, 234, 235, 237, 238, 240, 243, 244, 245, 246, 247, 249, 251, 252, 253, 255, 258, 261, 262, 264, 267, 270, 273, 275, 276, 281}

 

[1, 34] = P[104], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 95, 97, 100, 101, 103, 106, 108, 110, 113, 115, 116, 118, 120, 122, 126, 132, 134, 138, 141, 147, 152, 160, 161, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 219, 220, 222, 223, 225, 226, 228, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 248, 249, 251, 252, 254, 255, 257, 258, 260, 261, 264, 267, 270, 273, 276}

 

[1, 36] = P[110], {10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 117, 118, 120, 121, 124, 125, 129, 134, 135, 136, 138, 139, 141, 142, 144, 145, 147, 150, 151, 154, 156, 162, 171, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 225, 226, 227, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281}

 

[1, 38] = P[116], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 120, 121, 124, 125, 129, 135, 136, 141, 147, 150, 156, 158, 165, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 256, 258, 261, 262, 264, 267, 268, 270, 273, 274, 275, 276, 279, 282}

 

[1, 40] = P[122], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 124, 126, 129, 135, 136, 141, 147, 153, 156, 159, 160, 163, 166, 168, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 242, 243, 244, 245, 246, 247, 249, 251, 252, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281}

 

[1, 42] = P[128], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 130, 132, 138, 143, 144, 150, 153, 154, 157, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 256, 258, 261, 262, 264, 267, 270, 272, 273, 276, 278, 279, 281, 282}

 

[1, 44] = P[134], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 138, 140, 144, 150, 159, 162, 168, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 249, 250, 251, 252, 253, 255, 256, 258, 261, 262, 264, 267, 268, 270, 273, 275, 276, 281}

 

[1, 46] = P[140], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 159, 162, 168, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 249, 250, 251, 252, 253, 255, 257, 258, 261, 262, 264, 267, 268, 270, 273, 275, 276, 277}

 

[1, 48] = P[146], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 155, 156, 159, 162, 165, 166, 168, 172, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 229, 231, 233, 234, 235, 237, 238, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 269, 270, 273, 275, 276, 281}

 

[1, 50] = P[152], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 156, 159, 160, 162, 171, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 232, 233, 234, 235, 237, 238, 240, 241, 243, 244, 245, 246, 248, 251, 252, 254, 255, 257, 258, 260, 261, 263, 264, 267, 270, 273, 276}

 

[1, 52] = P[158], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 157, 160, 163, 165, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 232, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281, 282}

 

[1, 54] = P[164], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 157, 160, 162, 163, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 229, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 250, 251, 252, 254, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281, 282}

 

[1, 56] = P[170], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 157, 160, 162, 163, 165, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 255, 258, 261, 264, 266, 267, 270, 273, 275, 276, 279, 281}

 

[1, 58] = P[176], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 157, 160, 162, 163, 165, 171, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 238, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 280, 282}

 

[1, 60] = P[182], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 157, 160, 162, 163, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 238, 240, 243, 244, 245, 246, 247, 249, 251, 252, 255, 258, 261, 264, 267, 268, 270, 273, 276, 279, 282, 285}

 

[1, 62] = P[188], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 156, 168, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 228, 229, 231, 233, 234, 235, 236, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 265, 267, 270, 273, 275, 276, 279, 281}

 

[1, 64] = P[194], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 153, 156, 157, 160, 162, 163, 171, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 225, 226, 228, 229, 231, 233, 234, 235, 237, 240, 242, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281}

 

[1, 66] = P[200], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 132, 137, 141, 144, 150, 153, 157, 168, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 250, 251, 252, 253, 255, 258, 261, 262, 264, 267, 270, 273, 275, 276, 277, 279, 282}

 

[1, 68] = P[206], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 128, 133, 138, 141, 144, 150, 156, 157, 159, 160, 162, 168, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 268, 270, 273, 275, 276, 279, 282}

 

[1, 70] = P[212], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 126, 132, 135, 138, 141, 145, 150, 153, 157, 159, 161, 165, 166, 168, 171, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 249, 250, 251, 252, 255, 258, 261, 264, 267, 270, 275, 281}

 

[1, 72] = P[218], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 112, 114, 118, 119, 121, 122, 124, 126, 132, 133, 138, 141, 144, 150, 159, 166, 169, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 219, 220, 221, 222, 223, 224, 225, 226, 228, 231, 233, 234, 235, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 259, 260, 261, 263, 264, 266, 267, 269, 270, 272, 273, 276, 279}

 

[1, 74] = P[224], {3, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 101, 103, 105, 107, 109, 113, 114, 116, 117, 121, 122, 124, 126, 129, 135, 141, 143, 147, 152, 153, 160, 165, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 219, 220, 221, 222, 226, 228, 231, 233, 234, 235, 237, 240, 241, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 268, 270, 271, 273, 275, 276, 279, 281, 282}

 

[1, 76] = P[230], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 92, 93, 95, 97, 100, 102, 103, 105, 107, 109, 111, 116, 117, 120, 121, 123, 125, 127, 131, 135, 141, 143, 144, 148, 153, 156, 157, 163, 168, 169, 171, 172, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 228, 229, 231, 233, 234, 235, 236, 237, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 264, 267, 270, 273, 275, 276, 290}

 

[1, 78] = P[236], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 88, 89, 91, 93, 95, 97, 100, 103, 104, 107, 108, 110, 113, 114, 116, 118, 120, 122, 126, 128, 134, 135, 139, 141, 147, 150, 153, 156, 159, 162, 165, 167, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 217, 218, 219, 220, 223, 225, 226, 228, 229, 231, 232, 233, 234, 235, 237, 238, 240, 243, 244, 245, 246, 247, 251, 252, 253, 255, 258, 261, 262, 264, 267, 268, 270, 273, 275, 276, 281}

 

[1, 80] = P[242], {7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 75, 79, 81, 82, 84, 85, 87, 90, 91, 96, 97, 99, 100, 102, 104, 107, 109, 110, 112, 114, 117, 120, 121, 125, 126, 127, 130, 131, 138, 141, 144, 150, 152, 153, 154, 159, 163, 166, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 228, 229, 231, 234, 235, 236, 237, 238, 241, 243, 244, 245, 246, 247, 249, 251, 252, 253, 255, 258, 261, 262, 264, 267, 270, 272, 273, 275, 276, 281}

 

[1, 82] = P[248], {7, 10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 62, 63, 65, 67, 70, 71, 73, 76, 77, 79, 81, 83, 85, 88, 90, 92, 93, 96, 97, 99, 102, 103, 105, 107, 108, 109, 110, 112, 113, 117, 118, 121, 122, 126, 127, 132, 133, 136, 138, 144, 147, 150, 156, 158, 162, 168, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 221, 222, 226, 227, 229, 230, 232, 234, 235, 237, 238, 240, 241, 243, 244, 246, 249, 251, 252, 253, 255, 258, 261, 262, 264, 267, 270, 271, 273, 275, 276, 280, 281}

 

[1, 84] = P[254], {7, 10, 14, 16, 19, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 51, 53, 55, 58, 59, 61, 63, 65, 68, 69, 71, 72, 73, 74, 76, 79, 81, 82, 85, 86, 91, 93, 94, 96, 97, 99, 101, 103, 108, 109, 110, 111, 113, 115, 118, 120, 124, 127, 132, 133, 135, 141, 144, 147, 148, 150, 151, 153, 154, 156, 159, 162, 165, 168, 169, 171, 172, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 219, 220, 221, 222, 223, 224, 226, 228, 230, 231, 232, 234, 235, 239, 240, 242, 246, 247, 249, 250, 252, 255, 258, 261, 264, 267, 270, 273, 275, 276, 279, 281}

 

[1, 86] = P[260], {10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 52, 53, 55, 58, 60, 63, 64, 67, 68, 70, 71, 74, 75, 77, 79, 80, 81, 82, 85, 87, 89, 93, 94, 96, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 126, 127, 132, 133, 135, 141, 142, 144, 150, 151, 153, 159, 162, 163, 165, 166, 172, 174, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 222, 223, 224, 228, 229, 231, 232, 234, 235, 236, 239, 240, 241, 243, 246, 247, 248, 249, 251, 253, 254, 255, 258, 261, 263, 264, 267, 270, 272, 273, 275, 276, 281}

 

[1, 88] = P[266], {12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 36, 37, 38, 40, 43, 46, 47, 49, 52, 53, 55, 57, 59, 61, 63, 65, 67, 68, 71, 72, 74, 76, 79, 80, 82, 84, 87, 88, 91, 93, 94, 96, 100, 102, 103, 104, 108, 109, 111, 113, 117, 119, 121, 123, 127, 128, 135, 141, 145, 147, 151, 152, 153, 157, 161, 162, 163, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 220, 222, 223, 225, 228, 229, 231, 233, 237, 238, 239, 240, 244, 246, 247, 252, 253, 254, 255, 258, 261, 263, 264, 267, 268, 269, 270, 273, 275, 276, 281}

 

[1, 90] = P[272], {10, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 35, 39, 40, 41, 43, 46, 49, 50, 51, 52, 54, 55, 58, 59, 60, 62, 65, 66, 68, 71, 73, 76, 77, 79, 80, 84, 85, 87, 90, 91, 94, 97, 99, 100, 101, 103, 106, 109, 110, 111, 112, 113, 114, 115, 117, 120, 121, 123, 129, 130, 132, 138, 144, 147, 148, 150, 153, 155, 162, 163, 168, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 217, 219, 220, 222, 223, 224, 225, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 240, 243, 244, 246, 247, 250, 251, 252, 254, 259, 261, 263, 264, 267, 268, 269, 270, 273, 276}

 

[1, 92] = P[278], {4, 7, 10, 12, 14, 15, 16, 19, 21, 22, 25, 28, 29, 31, 34, 36, 37, 39, 41, 43, 46, 47, 49, 51, 55, 56, 58, 59, 60, 64, 65, 67, 69, 71, 73, 74, 79, 81, 82, 83, 85, 87, 89, 91, 94, 96, 97, 100, 101, 104, 105, 107, 111, 114, 115, 116, 118, 120, 122, 124, 126, 130, 135, 138, 141, 144, 154, 157, 159, 168, 169, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 216, 217, 219, 221, 223, 224, 225, 226, 228, 230, 231, 233, 237, 239, 240, 241, 243, 244, 246, 247, 249, 252, 253, 254, 255, 259, 261, 263, 264, 267, 270, 273, 275, 276, 279, 281, 282}

 

[1, 94] = P[284], {3, 4, 7, 10, 12, 14, 15, 16, 19, 22, 24, 25, 28, 30, 31, 34, 35, 36, 39, 41, 43, 46, 47, 49, 52, 53, 55, 58, 59, 61, 63, 66, 67, 70, 71, 73, 76, 78, 79, 82, 84, 85, 88, 90, 93, 95, 97, 99, 101, 103, 106, 108, 110, 112, 115, 118, 120, 121, 123, 127, 129, 135, 138, 139, 144, 145, 150, 156, 157, 159, 166, 168, 171, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 216, 217, 219, 220, 222, 223, 225, 226, 227, 228, 229, 231, 232, 234, 235, 237, 238, 239, 240, 241, 242, 243, 246, 247, 251, 252, 254, 255, 257, 258, 260, 261, 264, 267, 269, 270, 273, 274, 275, 279}

 

[1, 96] = P[290], {7, 10, 12, 13, 16, 17, 20, 21, 23, 25, 27, 29, 31, 32, 35, 37, 39, 43, 44, 46, 48, 49, 52, 53, 55, 58, 60, 61, 64, 65, 66, 67, 69, 70, 73, 75, 77, 80, 81, 84, 85, 88, 89, 91, 94, 96, 98, 101, 102, 104, 106, 109, 111, 112, 114, 116, 118, 121, 124, 126, 127, 129, 133, 135, 141, 142, 144, 150, 156, 161, 163, 166, 168, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 219, 220, 222, 224, 226, 229, 230, 231, 232, 234, 236, 237, 238, 239, 243, 244, 245, 246, 247, 249, 250, 251, 252, 255, 256, 258, 261, 264, 266, 267, 270, 273, 276, 279, 285}

 

[1, 98] = P[296], {8, 10, 13, 17, 19, 20, 22, 25, 27, 29, 31, 32, 34, 37, 38, 39, 41, 42, 43, 45, 46, 49, 51, 52, 54, 57, 58, 61, 63, 64, 67, 68, 73, 74, 76, 77, 78, 82, 83, 85, 88, 89, 92, 94, 95, 97, 101, 102, 106, 108, 109, 110, 112, 115, 118, 119, 120, 121, 124, 126, 127, 132, 135, 137, 138, 144, 145, 150, 156, 162, 165, 166, 169, 171, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 216, 217, 218, 219, 220, 222, 223, 225, 226, 227, 228, 230, 231, 232, 233, 234, 236, 237, 240, 241, 245, 246, 247, 248, 249, 252, 253, 254, 258, 260, 264, 267, 269, 270, 273, 276, 279}

 

[1, 100] = P[302], {6, 8, 10, 13, 15, 17, 19, 20, 22, 25, 27, 29, 31, 32, 34, 37, 38, 39, 41, 42, 43, 45, 46, 49, 51, 52, 54, 57, 58, 61, 63, 64, 67, 68, 71, 72, 74, 76, 78, 80, 82, 84, 87, 88, 91, 92, 94, 96, 98, 100, 102, 104, 106, 109, 112, 113, 115, 117, 119, 121, 126, 128, 132, 136, 144, 150, 157, 165, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 219, 220, 222, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 237, 239, 241, 243, 244, 246, 248, 252, 253, 254, 258, 259, 260, 264, 265, 267, 268, 270, 273, 276, 278, 279, 282}

 

numsols = 51

(7)

 


Download putnam2018.mw

 

Edit.
Maple can be also very useful in solving the difficult problem B6; it can be reduced to compute the (huge) coefficient of x^1842 in the polynomial

g := (1 + x + x^2 + x^3 + x^4 + x^5 + x^9)^2018;

The computation is very fast:

coeff(g, x, 1842):   evalf(%);
        
0.8048091229e1147

 

 

While generating a 3D plot of the solution of an ODE with a parameter, I noticed that better performance could be obtained by calling the plot3d command with a procedure argument, done in a special manner.

I don't recall this being discussed before, so I'll share it. (It it has been discussed, and this is widely known, then I apologize.)

I tweaked the initial conditions of the original ODE system, to obtain a non-trivial solution. I don't think that the particular nature of the solution has a bearing on this note.

restart;

Digits := 15:

 

 

The ODE system has two parameters. One, A, will get a fixed value. The

other, U0, will be used like an independent variable for plotting.

 

 

eq1:= diff(r[1](t), t, t)+(.3293064114+209.6419478*U0)*(diff(r[1](t), t))
      +569.4324330*r[1](t)-0.3123434112e-2*V(t) = -1.547206836*U0^2*q(t):
eq2:= 2.03*10^(-8)*(diff(V(t), t))+4.065040650*10^(-11)*V(t)
      +0.3123434112e-2*(diff(r[1](t), t)) = 0:
eq3 := diff(q(t), t, t)+1047.197552*U0*(q(t)^2-1)*(diff(q(t), t))
       +1.096622713*10^6*U0^2*q(t) = -2822.855019*A*(diff(r[1](t), t, t)):

 

ics:=r[1](0)=0,D(r[1])(0)=1e-1,V(0)=0,q(0)=0,D(q)(0)=0:

 

res := dsolve({eq1,eq2,eq3, ics},numeric,output=listprocedure,parameters=[A,U0]):

 

I will call the procedure returned by dsolve, for evalutions of V(t), as the

dsolve numeric solution-procedure in the discussion below.

 

WV := eval(V(t), res):

 

WV(parameters=[A=1e0]):

 

 

The goal is to produce a 3D plot of V(t) as a function of t and the parameter U0.

 

 

tlo,thi := 0.0, 2.0;
U0lo,U0hi := 1e-3, 2e-1;

0., 2.0

0.1e-2, .2

 

This is the grid size used for plot3d below. It is nothing special.

 

(m,n) := 51,51;

51, 51

 

First, I'll demonstrate that a 3D plot can be produced quickly, by populating a
Matrix for floating-point evaluations of V(t), depending on t in the first
Matrix-dimension and on parameter U0 in the second Matrix-dimansion.

 

The surfdata command is used. This is similar to how plot3d works.

 

This  computes reasonably quickly.

 

But generating the numeric values for U0 and t , based on the i,j positions

in the Matrix, involves the kind of sequence generation formulas that are

error prone for people.

 

str := time[real]():
M:=Matrix(m,n,datatype=float[8]):
for j from 1 to n do
  u0 := U0lo+(j-1)*(U0hi-U0lo)/(n-1);
  WV(parameters=[U0=u0]);
  for i from 1 to m do
    T := tlo+(i-1)*(thi-tlo)/(m-1);
    try
      M[i,j] := WV(T);
    catch:
      # mostly maxfun complaint for t above some value.
      M[i,j] := Float(undefined);
    end try;
  end do:
end do:
plots:-surfdata(M, tlo..thi, U0lo..U0hi,
                labels=["t","U0","V(t)"]);
(time[real]()-str)*'seconds';

1.686*seconds

 

So let's try it using the plot3d command directly. A 2-parameter procedure
is constructed, to pass to plot3d. It's not too complicated. This procedure
will uses one of its numeric arguments to set the ODE's U0 parameter's

value for the dsolve numeric solution-procedure, and then pass along

the other numeric argument as a t value.


It's much slower than the surfdata call above..

 

VofU0 := proc(T,u0)
       WV(parameters=[U0=u0]);
       WV(T);
     end proc:

str := time[real]():
plot3d(VofU0, tlo..thi, U0lo..U0hi,
       grid=[m,n], labels=["t","U0","V(t)"]);
(time[real]()-str)*'seconds';

37.502*seconds

 

One reason why the previous attempt is slow is that the plot3d command

is changing values for U0 in its outer loop, and changing values of t in its

inner loop. The consequence is that the value for U0 changes for every

single evaluation of the plotted procedure. This makes the dsolve numeric

solution-procedure work harder, by losing/discarding prior numeric
solution details.

 

The simple 3D plot below demonstrates that the plot3d command chooses
x-y pairs by letting its second supplied independent variable be the one
that changes in its outer loop. Each time the value for y changes the counter

goes up by one.

 

glob:=0:
plot3d(proc(x,y) global glob; glob:=glob+1; end proc,
       0..3, 0..7, grid=[3,3],
       shading=zhue,  labels=["x","y","glob"]);

 

So now let's try and be clever and call the plot3d command with the two
independent variables reversed in position (in the call). That will make

the outer loop change t instead of the ODE parameter U0.

 

We can use the transform command to swap the two indepenent
axes in the plot, if we prefer the axes roles switched. Or we could use the
parametric calling sequence of plot3d for the same effect.

 

The problem is that this is still much slower!

 

VofU0rev := proc(u0,T)
       WV(parameters=[U0=u0]);
       WV(T);
     end proc:

str := time[real]():
Prev:=plot3d(VofU0rev, U0lo..U0hi, tlo..thi,
             grid=[n,m], labels=["U0","t","V(t)"]):
(time[real]()-str)*'seconds';

plots:-display(
  plottools:-transform((x,y,z)->[y,x,z])(Prev),
  labels=["t","U0","V(t)"],
  orientation=[50,70,0]);

34.306*seconds

 

There is something else to adjust, to get the quick timing while using

the plot3d command here.

 

It turns out that setting the parameter's numeric value in the
dsolve numeric solution-procedure causes the loss of previous details
of the numeric solving, even if the parameter's value is the same.

 

So calling the dsolve numeric solution-procedure to set the parameter

value must be avoided, in the case that the new value is the same as

the old value.

 

One way to do that is to have the plotted procedure first call the

dsolve numeric solution-procedure to query the current parameter

value, so as to not reset the value if it is not changed. Another way

is to use a local of an appliable module to store the running value

of the parameter, and check against that. I choose the second way.

 

And plot3d must still be called with the first independent variable-range

as denoting the ODE's parameter (instead of the ODE's independent

variable).

 

And the resulting plot is fast once more.

 

VofU0module := module()
       local ModuleApply, paramloc;
       ModuleApply := proc(par,var)
         if not (par::numeric and var::numeric) then
           return 'procname'(args);
         end if;
         if paramloc <> par then
           paramloc := par;
           WV(parameters=[U0=paramloc]);
         end if;
         WV(var);
       end proc:
end module:

 

For fun, this time I'll use the parameter calling sequence to flip the

axes, instead of plots:-transform. That's just because I want t displayed

on the first axis. But for the performance gain, what matters is that it

is U0 which gets values from the first axis plotting-range.

 

str := time[real]():
plot3d([y,x,VofU0module(x,y)], x=U0lo..U0hi, y=tlo..thi,
       grid=[n,m], labels=["t","U0","V(t)"]);
(time[real]()-str)*'seconds';

1.625*seconds

 

And, naturally, I could also use the parametric form to get a fast plot

with the axes roles switched.

 

str := time[real]():
plot3d([x,y,VofU0module(x,y)], x=U0lo..U0hi, y=tlo..thi,
       grid=[n,m], labels=["U0","t","V(t)"]);
(time[real]()-str)*'seconds';

1.533*seconds

 

Download ode_param_plot.mw

I am preparing a Slideshow with Maple 2018.2
I want to use a small laptop to do the presentation with MaplePlayer 2018.1 without purchasing and installing the hole stuff.

The presentation contains some 3d animated plots controlled by some DocumentTools,Components,Button components just
to start and stop the animations during my talk.

The Player dont appear to run (!!!)  the worksheet at startup, so the Plot components dont get an identity and the Button components dont get the Plot components identity neither to set their "play" property. As a consequence Button components appear useless.

Is there any mean to make this work?

Thanks.

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

 

Hello,

I cannot find a solution for multiplying matrices containing vectors. I seems that matrix operations are not overloaded for accepting vectors. Here is a minimum example :

restart;
with(LinearAlgebra);
with(VectorCalculus);
A := Matrix([u, v]);
B := Transpose(A) . A;

# Entries of A are in fact vectors
u := `<,>`(u1, u2);
v := `<,>`(v1, v2);

# Here are the expected entries of matrix B

u . u;
v . v;
u . v;

# but entries cannot be calculated
simplify(B);

B := Transpose(A) . A;

Of course I can obtain the result if I construct the matrix A with the components of u and v but  my goal is to manipulate more concise expressions with vectors rather than components. May I find a solution in some other package ?

Would it be a complicated task to develop the missing operators or tell Maple to use the dot operator (for matrices and vector) when performing matrix multiplication ?

Thanks for your insights.

 K is a function by K(u,ux), and there is an equation K2,2=0,. It must be solved like K=K1(u)*ux+k2(u)

Is there any command to help me solve that kind of expression just in Jet space?

Dear users,

Can any one give a correct model statement (if what I have suggested is incorrect) for each one of the following in a module:

module() export eseq;  local lseq;  global gseq;  option optseq; 

 description dseq;  uses usesSequence;  statementSequence   end

My model statements:

export x1, y1;

# x1 and y1 are variables calculated here and sent to main document

 local a, b;  

# a and b are local constants are variables used here inside module only


global z1; 

# z1 is a constant or variable used all over the document can be read from and exported to main document and used in manipulation anywhere in the main document as well as inside the module.

option if x1 = .. else... end; 

 description dseq;

# Statements for self use and understanding the commands during execution

 usesSequence;

uses DocumentTools;

# Packages used in module like DocumentTools, Students Calculus

Statement Sequence

valid executable maple command  1

valid executable maple command  last

 

I want to understand the basic usage of  a module and procedure with a simple document.  

I am also confused over the following.


1) Is there any use of a module with zero statement (as given below) in it?

 module ()

end module

2) What is the major difference between module and procedure?

3) What is in module that is not possible in procedure?
I believe that procedure is like a function [for call from script(internally or eternally) or command window] in MATLAB and subroutine in FORTRAN or BASIC etc. What is module like in other programme siftwares?

Thanks for helping.

Ramakrishnan V


 

@tomleslie 

Dear Tom,

I need your help. I have a delay differential equation to solve and extract the value of the solution y(t) at a selected point of the independent variable t.  I am uploading a small sample code. 

Thanks.
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw

 

Hi everyone: 

I want to obtain r1(t), V(t) , q(t) in terms of U0 and plot V(t) in terms of U0, how? 

eq1:= diff(r[1](t), t, t)+(.3293064114+209.6419478*U[0])*(diff(r[1](t), t))+569.4324330*r[1](t)-0.3123434112e-2*V(t) = -1.547206836*U[0]^2*q(t)
eq2:= 2.03*10^(-8)*(diff(V(t), t))+4.065040650*10^(-11)*V(t)+0.3123434112e-2*(diff(r[1](t), t)) = 0
eq3 := diff(q(t), t, t)+1047.197552*U[0]*(q(t)^2-1)*(diff(q(t), t))+1.096622713*10^6*U[0]^2*q(t) = -2822.855019*(diff(r[1](t), t, t))
ics:=r1(0)=0,D(r1)(0)=0,V(0)=0,q(0)=0,D(q)(0)=0;

Tnx...

Hi, everytimes I enter anythings, it turn out with Typesetting:-mparsed( bla1bla2, bla1bla2;"_noterminate")

example:

For an Array A, say, and some positive integer n, say, Maple interpretes A^n as raising each entry separately to the same power n. Without the Physics package loaded, A^n can also be written as A . A . ... . A (n times). But with the Physics package loaded, this equality is broken (at least in Maple 2017): If A is a 2D square Array, A . A all of a sudden is no longer equal to A^2, but rather to convert(A,Matrix)^2, i.e., to the square of the Array considered as a Matrix. The presence of the dot operator seems to make the Physics enviroment convert A to a Matrix. This seems to me to be a bug.

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