Carl Love

Carl Love

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9 years, 309 days
Natick, Massachusetts, United States
My name was formerly Carl Devore.

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These are answers submitted by Carl Love

Like this:

W:= `[]`~(P, Q);

An operator is called a binary infix operator if it can take 2 arguments and can be placed between (rather than in front of) them. So, most familar arithmetic operators (such as +, -, *, /, =, <, ^, and others) are binary infix operators. The way that you wrote your Question suggests that you want to use oper in infix form. This is easy in Maple, and it's one of my favorite features of Maple's syntax. The operator's name should begin with &, followed by letters or a wide variety of punctuation marks.

AnyOp:= proc(`&op`, x, y) x &op y end proc:
AnyOp(`*`, 7, 3), AnyOp(`+`, 7, 3); 

                             
21, 10

When the operator is not being used in infix form, it must be in back quotes (notice `&op` immediately after proc). This is true for all infix operators, not just those beginning with (notice `*` and `+` above). On the other hand, when they are used in infix form, they must NOT have quotes.

In the examples above, the operation that is passed to `&op` need not be infix as long as it can accept two arguments (see iquo and irem below):

AnyOp:= (`&?`, x, y)-> x &? y:
AnyOp~([`*`, `+`, `-`, `/`, `mod`, iquo, irem, `^`], 7, 3);

                  [21, 10, 4, 7/3, 1, 2, 1, 343]

Since mod is one of Maple's infix operators, even though it's just alphabetic characters, it needs the quotes when it's passed.

 

The plot can be made perfectly (no gaps, no jaggedness) and easily (no fancy options or extra points or precision needed) by these steps:

  1. Express your Watt equation as an expression implicitly equated to 0.
  2. Convert the expression from polar coordinates to Cartesian (x,y). (There's a command for that, but rather than looking up its syntax, I just used the usual well-known substitutions.)
  3. Rationalize the resulting algebraic function with evala@Norm. (The resulting rational function can be simplified significantly, which might be useful if you're going to do further algebra on it; but, it plots with no trouble without simplification.)
  4. Put in your numeric parameters.
  5. Plot with implicitplot.
restart:
WattEq:= r^2 - (b^2 - (a*sin(theta) + sqrt(c^2 - a^2*cos(theta)^2))^2);
params:= [a= 3.1, b= 1.1, c= 3.]:  rng:= -1.2..1.2:
W:= (evala @ Norm @ eval[recurse])(
    WattEq,
    #polar to cartesian: 
    [r= sqrt(x^2+y^2), (cos,sin)(theta)=~ (x,y)/~r]
);
  

plots:-implicitplot(eval(W, params), (x,y)=~ rng, scaling= constrained);

The most-basic way to remove specific cases of inertness is to change a name beginning with % to the equivalent name without a %. Thus, this handles your case:

Set:= eval({op}(InertForm:-Parse(Str)), %Vector= Vector);
InertForm:-ToMathML(`%+`(Set[]));

 

Here are two procedures: The first detects whether its argument is an overload, and the second deconstructs an overloaded argument into its original procedures.

IsOverload:= (P::procedure)-> 
    evalb(indets(ToInert(eval(P)), specfunc(_Inert_OVERLOADLIST)) <> {})
:
UnOverload:= (P::And(procedure, satisfies(IsOverload)))->
    indets(
        subsindets(
            ToInert(eval(P)), 
            specfunc(_Inert_OVERLOADLIST), 
            %overload@[FromInert]@op
        ),
        specfunc(%overload)
    )[-1]
:

#Example usage:

P:= overload([
    proc(n::And(posint, even)) option overload; n/2 end proc,
    proc(n::And(posint, odd)) option overload; 3*n+1 end proc,
    proc(n) 'procname'(args) end proc
]);
P := overload(
  [
  proc (n::(And(posint, even))) option overload; (1/2)*n end proc, 
  proc (n::(And(posint, odd))) option overload; 3*n+1 end proc, 
  proc (n) ('procname')(args) end proc])

IsOverload~([P, cos]);
                         [true, false]
UnOverload(P);
%overload(
  [
  proc (n::(And(posint, even))) option overload; (1/2)*n end proc, 
  proc (n::(And(posint, odd))) option overload; 3*n+1 end proc, 
  proc (n) ('procname')(args) end proc])

 

Replace with %*:

P:= a %* b %* c %* d %* e;

In your 7-year-old version of Maple, you may need to use prefix form:

P:= `%*`(a, b, c, d, e);

Here's another way to do the unit conversion on a vector or matrix that I suspect is closer to what you were originally trying. Enter your vector, highlight and right click, do the unit conversion as you originally tried. When that's done, the vector will appear unchanged, as you initially reported. Now, give the command

rtable_eval(%);

The unit-converted vector should now appear.

The issue here is somewhat like the rtablesize issue that I wrote about an hour ago in the sense that the computations are already done but you're not seeing the results; however, in this case the issue doesn't only affect the display. (It took me many years to fully understand the rtable_eval command, so you'll likely need to just accept that it's the "magic command" that does what you want in this case.)

What you described is indeed an efficient (although somewhat mysterious) way to fill a matrix. It doesn't matter whether the entries are floats or any other type. The key step is to use the very mysterious command rtable_eval on the row vector; it changes the symbolic variables (ABC, etc.) in the row vector to their assigned values. Like this:

restart:
OutVec:= <A, B, C>^%T: #row vector
OutMat:= Matrix((9, numelems(OutVec)), datatype= anything):
#The datatype could be hfloat or anything else or omitted entirely.

MyFuncs:= proc(k)
    :-A:= (k-1)^2;
    :-B:= k^2;
    :-C:= (k+1)^2;
    rtable_eval(OutVec)
end proc
:
for k to upperbound(OutMat)[1] do
    OutMat[k]:= MyFuncs(k)
od
:
OutMat;

Whether you send this matrix to Excel afterwards is irrelevant; that'd be handled exactly like sending any matrix to Excel, e.g., as shown by @dharr .

I can't tell you how to do it with context-menu-based commands such as you appear to be using, but these text-based commands do it:

convert~(<20., 30., 40.>*Unit(MPa), units, psi);
convert~(<150., 300., 600.>*Unit(psi), units, MPa);

Note the ~ after convert, which causes the command to be applied elementwise to the vector. It works exactly the same for a matrix, array, list, set, or table.

What you describe should be fairly easy because Maple (since Maple 2018) has an on-board Python interpreter and a small package of commands to support it. See help page ?Python.

It's easier to write a procedure for this that works for an arbitrary number of arguments than it is to write one specific to 4 arguments. In the procedure below, you'll need to fill in the ...'s.

biggest4:= proc(S::seq(realcons)) #i.e., the arguments will be a SEQuence of REAL CONStants
local 
    M:= S[1], #Initialize max to 1st argument (arbitrarily).
    x #any of the arguments
;
    #Compare every argument to the max computed so far and adjust it if needed:
    for x in S do
        #The "is" command is sometimes needed to compare complicated symbolic
        #expressions that represent real numbers:
        if is(x > ...) then ...:= ... fi 
    od;
    M #procedure's return value
end proc
:
biggest4(-1/3, 0, 7/3, -2);

If you omit the is, this'll still work for these example numbers.

I'm sure that you know the standard techniques, so I wonder why they're working for me but not for you:

S:= select(type, [solve](diff(F,z), z), realcons);
allvalues(S[min[index](eval~(F, z=~ S))]);

 

@mehdibgh It should come as no surprise that fff has some negative values. So, sqrt(fff) has some imaginary values. To check, extract the min and max values from the data matrix of a plot of fff (not sqrt(fff)):

(min, max)(op([1,3], plot3d(fff, zeta__1= -1..1, eta__1= -1..1)));
              -1.68517697876451*10^(-7), 0.000874224224310557

So the negative values have relatively small magnitude, but they are there nonetheless. If fff has been constructed to be positive valued, then these negatives are from rounding errors in the huge number of floating-point calculations. In this case, just ignore the imaginary parts.

I'm amazed that anyone finds these imaginary parts surprising!

1) Plotting them all: This can be done by using plots:-display on a matrix of individual plots.

2) Finding equivalence classes (under graph isomorphism or any other property): This can be done with ListTools:-Categorize; or, if you know a function that gives an equivalence class representative, it can be done more efficiently with ListTools:-Classify.

# This likely only works in 1D-input!
#
DrawGraphs:= (L::{list,set}(Graph))->
local n:= nops(L), c:= isqrt(n);
    (plots:-display@Matrix)(
        (ceil(n/c), c), 
        (i,j)-> local k:= (i-1)*c+j; 
            if k<=n then GraphTheory:-DrawGraph(L[k], 'title'= k, _rest)
            else plot('axes'= 'none')
            fi
    ):   
n:= 50:
LG:= ['GraphTheory:-RandomGraphs:-RandomGraph(6,7)' $ n]:
ListTools:-Categorize((i,j)-> GraphTheory:-IsIsomorphic(LG[i],LG[j]), [$1..n]);
# Indices in each sublist represent isomorphic graphs.
[1, 11, 14, 15, 18, 19, 23, 24, 36, 38], [2, 41, 47, 50], [3, 5], 
  [4, 13, 44, 46], [6], [7, 12, 25, 33, 39, 49], [8], [9, 27], 
  [10, 29], [16], [17, 40], [20, 31, 34], [21, 42], 
  [22, 28, 30, 32, 48], [26], [35], [37], [43], [45]

DrawGraphs(LG);

 

To avoid the dialogs regarding the axis names, you can set environment variables like this:

_Env || (Horizont, Vertic) || alName:= (x, y):

This only needs to be done once per session (per restart), and it doesn't matter whether you do it before or after with(geometry) or whether you use with(geometry) at all. If you use geometry a lot, and you always use x and as the coordinates, then it's worth putting that command in an initialization file. On the other hand, if you often use a variety of coordinate names, then you should use Christopher's Answer.

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