In Maple outputs, long fraction bars occur quite frequently. A common example is of the type A(x)/x, where A(x) may be a complicated expression made up by standard functions, derivatives, integrals etc. in terms of x and some constants, denoted by names. Maple displays such an expression in terms of a long solidus and x as the denominator. This looks rather weird. A preferable display would be of the form x^-1 A(x) or A(x) multiplied by 1/x. I have unsuccessfully tried to achieve this but failed. Can this be done?

For given positive integers 𝑎 and 𝑏, there exist positive integers 𝑟 and 𝑠 (the so-called *Bezout’s coefficients*) so that 𝑔𝑐𝑑(𝑎,𝑏)=𝑟 𝑎+𝑠 𝑏. Using Euclidean algorithm, one can find these coefficients by using a forward and a backward substitution. Surf the web, let say this one https://brilliant.org/wiki/bezouts-identity/, or use any Discreet Mathematics textbook to find out how these coefficient can be computed using Euclidean algorithm. Now, write a code in Maple to compute Bezout’s coefficients for the numbers 18344 and 65208.

I have two input variables namely torque and speed. I need to find the input current for the given induction motor. I have written down the required equations in math mode. So, when I give a specific input i.e. torque is 30 Nm and speed is 2000 rpm i get the input current. Now I need to put in a for loop for the math mode i.e. i need output current dataset for 10% increment in torque from zero to full torque and 10% increment in speed from 0 to full load speed. I cant seem to find any resource to do that in maple. Could anyone help me out?

;
restart; with(plots); _local(O);
P := b*x*cos(phi)+a*y*sin(phi)-a . b = 0;
P := b x cos(phi) + a y sin(phi) - a . b = 0
Q := a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi) = 0;
2
Q := a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) = 0
M := op(solve([P, Q], [x, y])); M := [subs(M, x), subs(M, y)];
X := `&-+`(P/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2)); Y := `&-+`(Q/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2));
#L'équation générale des coniques ayant pour axes MN et MT est, par rapport aux nouveaux axes de coordonnées
X^2/A+Y^2/B-1 = (0*et)*par*rapport*aux*anciens;
P^2/(A*(b^2*cos(phi)^2+a^2*sin(phi)^2))+Q^2/(B*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0;
2
/b x cos(phi) + a y sin(phi) - a . b \
&-+|----------------------------------- = 0|
| (1/2) |
|/ 2 2 2 2\ |
\\a sin(phi) + cos(phi) b / /
---------------------------------------------
A
2
/ 2 \
|a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) |
&-+|-------------------------------------------------- = 0|
| (1/2) |
| / 2 2 2 2\ |
\ \a sin(phi) + cos(phi) b / /
+ ------------------------------------------------------------
B
- 1 = 0
#1.-Ecrivons que la conique (1) est tangente en O à Oy : il faut pour cela annuler le coefficient de y et le terme indépendant.
#Nous obtenons 2 équations en A et B, d'où nous tirons : A=a² et B=c²cos(phi)²
a := 10; b := 7; c := sqrt(a^2-b^2); phi := 4*Pi*(1/5);
Ell := implicitplot(x^2/a^2+y^2/b^2-1 = 0, x = -11 .. 11, y = -8 .. 8, color = grey);
O := [0, 0]; M := [a*cos(phi), b*sin(phi)];
vec := plot([O, M], color = black, thickness = 1);
P := implicitplot(P, x = -20 .. 20, y = -20 .. 20, color = aquamarine);
Q := implicitplot(Q, x = -20 .. 20, y = -20 .. 20);
F1 := [(a+b)*cos(phi), (a+b)*sin(phi)]; F2 := [2*M[1]-F1[1], 2*M[2]-F1[2]];
F1F2 := plot([F1, F2], color = green, thickness = 3);
ELL := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(a^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(c^2*cos(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = blue, thickness = 3);
Hyp := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(b^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(-c^2*sin(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = black);
dF1 := plottools[disk](F1, .3, color = red);
dF2 := plottools[disk](F2, .3, color = red);
cir1 := implicitplot(x^2+y^2 = (a+b)^2, x = -20 .. 20, y = -18 .. 18, color = pink);
cir2 := implicitplot(x^2+y^2 = (a-b)^2, x = -10 .. 10, y = -4 .. 4, color = coral);
asym1 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
asym2 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b-(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
tp := textplot([[M[1], M[2]+.8, "M"], [F1[1]-.8, F1[2], "F1"], [F2[1]+.8, F2[2]+.3, "F2"], [5, 15, "axe P"], [8, -10, "axe Q"]]);
display([Ell, vec, P, Q, F1F2, cir1, cir2, ELL, Hyp, dF1, dF2, asym1, asym2, tp], scaling = constrained, axes = normal, axis = [gridlines = [1, color = blue]], xtickmarks = 0, ytickmarks = 0, view = [-20 .. 20, -20 .. 20], size = [500, 500]);
#Eléments fixes : Ell, cir1, cir2, O
#Parties mobiles : ELL, Hyp, P,Q, M,F1, F2,
# FIGURE MOBILE
n := 100; dt := 2*Pi/n; Phi := 0;
P := b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b = 0;
Q := a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt) = 0;
M := [cos(phi+dt)*(sin(phi+dt)^2*a*c^2+Typesetting[delayDotProduct](a . b, b, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2), sin(phi+dt)*(-cos(phi+dt)^2*b*c^2+Typesetting[delayDotProduct](a . b, a, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2)];
ELL := (b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b)^2/(a^2*(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2))+(a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt))^2/(c^2*cos(phi+dt)^2*(cos(phi+dt)^2*b^2+a^2))-1 = 0;
NULL;
display([Ell, cir1, cir2], scaling = constrained);