Dear Users!
First, I define the following polynomial as:

restart; with(LinearAlgebra); nu := 1/2; M1 := 3; M2 := 3; #(any value of M1 and M2)
for k1 from 0 while k1 <= M1-1 do for k2 from 0 while k2 <= M2-1 do
SGP[M2*k1+k2+1] := simplify(sum((-1)^(k1-i1)*GAMMA(k1+i1+2*nu)*GAMMA(nu+1/2)*x^i1*(sum((-1)^(k2-i2)*GAMMA(k2+i2+2*nu)*GAMMA(nu+1/2)*t^i2/(GAMMA(i2+nu+1/2)*factorial(k2-i2)*factorial(i2)*GAMMA(2*nu)), i2 = 0 .. k2))/(GAMMA(i1+nu+1/2)*factorial(k1-i1)*factorial(i1)*GAMMA(2*nu)), i1 = 0 .. k1))
end do end do;
Lambda := `<,>`(seq(SGP[i], i = 1 .. M1*M2));

then, I want to define a square matrix A of order M1M2 by M1M2 after collocating SGP[k](x,y) at x=(i-1)/(M1-1) and y=(j-1)/(M2-1) for i=1,2,3,...M1, j=1,2,3,...M2.

For example, for M1=2 and M3=3 this matrix A is given as:

A:=Matrix(6, 6, {(1, 1) = SGP[1](0, 0), (1, 2) = SGP[2](0, 0), (1, 3) = SGP[3](0, 0), (1, 4) = SGP[4](0, 0), (1, 5) = SGP[5](0, 0), (1, 6) = SGP[6](0, 0), (2, 1) = SGP[1](0, 1), (2, 2) = SGP[2](0, 1), (2, 3) = SGP[3](0, 1), (2, 4) = SGP[4](0, 1), (2, 5) = SGP[5](0, 1), (2, 6) = SGP[6](0, 1), (3, 1) = SGP[1](1/2, 0), (3, 2) = SGP[2](1/2, 0), (3, 3) = SGP[3](1/2, 0), (3, 4) = SGP[4](1/2, 0), (3, 5) = SGP[5](1/2, 0), (3, 6) = SGP[6](1/2, 0), (4, 1) = SGP[1](1/2, 1), (4, 2) = SGP[2](1/2, 1), (4, 3) = SGP[3](1/2, 1), (4, 4) = SGP[4](1/2, 1), (4, 5) = SGP[5](1/2, 1), (4, 6) = SGP[6](1/2, 1), (5, 1) = SGP[1](1, 0), (5, 2) = SGP[2](1, 0), (5, 3) = SGP[3](1, 0), (5, 4) = SGP[4](1, 0), (5, 5) = SGP[5](1, 0), (5, 6) = SGP[6](1, 0), (6, 1) = SGP[1](1, 1), (6, 2) = SGP[2](1, 1), (6, 3) = SGP[3](1, 1), (6, 4) = SGP[4](1, 1), (6, 5) = SGP[5](1, 1), (6, 6) = SGP[6](1, 1)});

for M1=3 and M=2 the matrix A is given as:

A:=Matrix(6, 6, {(1, 1) = SGP[1](0, 0), (1, 2) = SGP[2](0, 0), (1, 3) = SGP[3](0, 0), (1, 4) = SGP[4](0, 0), (1, 5) = SGP[5](0, 0), (1, 6) = SGP[6](0, 0), (2, 1) = SGP[1](0, 1/2), (2, 2) = SGP[2](0, 1/2), (2, 3) = SGP[3](0, 1/2), (2, 4) = SGP[4](0, 1/2), (2, 5) = SGP[5](0, 1/2), (2, 6) = SGP[6](0, 1/2), (3, 1) = SGP[1](0, 1), (3, 2) = SGP[2](0, 1), (3, 3) = SGP[3](0, 1), (3, 4) = SGP[4](0, 1), (3, 5) = SGP[5](0, 1), (3, 6) = SGP[6](0, 1), (4, 1) = SGP[1](1, 0), (4, 2) = SGP[2](1, 0), (4, 3) = SGP[3](1, 0), (4, 4) = SGP[4](1, 0), (4, 5) = SGP[5](1, 0), (4, 6) = SGP[6](1, 0), (5, 1) = SGP[1](1, 1/2), (5, 2) = SGP[2](1, 1/2), (5, 3) = SGP[3](1, 1/2), (5, 4) = SGP[4](1, 1/2), (5, 5) = SGP[5](1, 1/2), (5, 6) = SGP[6](1, 1/2), (6, 1) = SGP[1](1, 1), (6, 2) = SGP[2](1, 1), (6, 3) = SGP[3](1, 1), (6, 4) = SGP[4](1, 1), (6, 5) = SGP[5](1, 1), (6, 6) = SGP[6](1, 1)});

and for M1=M2=3 the matrix A should be the following form:

A:=Matrix(9, 9, {(1, 1) = SGP[1](0, 0), (1, 2) = SGP[2](0, 0), (1, 3) = SGP[3](0, 0), (1, 4) = SGP[4](0, 0), (1, 5) = SGP[5](0, 0), (1, 6) = SGP[6](0, 0), (1, 7) = SGP[7](0, 0), (1, 8) = SGP[8](0, 0), (1, 9) = SGP[9](0, 0), (2, 1) = SGP[1](0, 1/2), (2, 2) = SGP[2](0, 1/2), (2, 3) = SGP[3](0, 1/2), (2, 4) = SGP[4](0, 1/2), (2, 5) = SGP[5](0, 1/2), (2, 6) = SGP[6](0, 1/2), (2, 7) = SGP[7](0, 1/2), (2, 8) = SGP[8](0, 1/2), (2, 9) = SGP[9](0, 1/2), (3, 1) = SGP[1](0, 1), (3, 2) = SGP[2](0, 1), (3, 3) = SGP[3](0, 1), (3, 4) = SGP[4](0, 1), (3, 5) = SGP[5](0, 1), (3, 6) = SGP[6](0, 1), (3, 7) = SGP[7](0, 1), (3, 8) = SGP[8](0, 1), (3, 9) = SGP[9](0, 1), (4, 1) = SGP[1](1/2, 0), (4, 2) = SGP[2](1/2, 0), (4, 3) = SGP[3](1/2, 0), (4, 4) = SGP[4](1/2, 0), (4, 5) = SGP[5](1/2, 0), (4, 6) = SGP[6](1/2, 0), (4, 7) = SGP[7](1/2, 0), (4, 8) = SGP[8](1/2, 0), (4, 9) = SGP[9](1/2, 0), (5, 1) = SGP[1](1/2, 1/2), (5, 2) = SGP[2](1/2, 1/2), (5, 3) = SGP[3](1/2, 1/2), (5, 4) = SGP[4](1/2, 1/2), (5, 5) = SGP[5](1/2, 1/2), (5, 6) = SGP[6](1/2, 1/2), (5, 7) = SGP[7](1/2, 1/2), (5, 8) = SGP[8](1/2, 1/2), (5, 9) = SGP[9](1/2, 1/2), (6, 1) = SGP[1](1/2, 1), (6, 2) = SGP[2](1/2, 1), (6, 3) = SGP[3](1/2, 1), (6, 4) = SGP[4](1/2, 1), (6, 5) = SGP[5](1/2, 1), (6, 6) = SGP[6](1/2, 1), (6, 7) = SGP[7](1/2, 1), (6, 8) = SGP[8](1/2, 1), (6, 9) = SGP[9](1/2, 1), (7, 1) = SGP[1](1, 0), (7, 2) = SGP[2](1, 0), (7, 3) = SGP[3](1, 0), (7, 4) = SGP[4](1, 0), (7, 5) = SGP[5](1, 0), (7, 6) = SGP[6](1, 0), (7, 7) = SGP[7](1, 0), (7, 8) = SGP[8](1, 0), (7, 9) = SGP[9](1, 0), (8, 1) = SGP[1](1, 1/2), (8, 2) = SGP[2](1, 1/2), (8, 3) = SGP[3](1, 1/2), (8, 4) = SGP[4](1, 1/2), (8, 5) = SGP[5](1, 1/2), (8, 6) = SGP[6](1, 1/2), (8, 7) = SGP[7](1, 1/2), (8, 8) = SGP[8](1, 1/2), (8, 9) = SGP[9](1, 1/2), (9, 1) = SGP[1](1, 1), (9, 2) = SGP[2](1, 1), (9, 3) = SGP[3](1, 1), (9, 4) = SGP[4](1, 1), (9, 5) = SGP[5](1, 1), (9, 6) = SGP[6](1, 1), (9, 7) = SGP[7](1, 1), (9, 8) = SGP[8](1, 1), (9, 9) = SGP[9](1, 1)});

Please help to define general matrix A for any values of M1 and M2. I will be very grateful for you. 

When I am using

Polynomialdeal package:

sys:=[p31,p32,p33];

as in the end of the post. (for one to reproduce)

`J := PolynomialIdeal(sys, characteristic = p)`

and calculate the corresponding Groebner basis.

It report this "Error, (in Groebner:-Basis) Segmentation Violation occurred in external routine".

Does anyone know how to fix this error?

Here is the output details.

infolevel[GroebnerBasis] := 5;

 GB:=Groebner[Basis](sys,IdealInfo[DefaultMonomialOrder](J),method=fgb);

memory used=712.9MB, alloc=103.8MB, time=4.48
memory used=779.3MB, alloc=111.8MB, time=4.89
-> MGb
 domain: rat_int_cof
F4 algorithm
1: prime=2132425153
 deg  pairs  taken         matrix                                        found
   6     20      1         8 x 1018       238.5 per row,     0.0 MB      1 new,      0 zero     0.007 sec
   8     22      3       310 x 20321      288.7 per row,     0.7 MB      3 new,      0 zero     0.035 sec
   9     28      5       818 x 38796      397.2 per row,     2.5 MB      5 new,      0 zero     0.069 sec
  10     37     18      5118 x 220200     532.9 per row,    20.8 MB     16 new,      2 zero     0.386 sec
  11     83     52     21117 x 653954     835.4 per row,   134.7 MB     35 new,     17 zero     1.844 sec
  12    218    153     84758 x 2148937   1314.0 per row,   850.0 MB    100 new,     53 zero    14.546 sec
  13    690    551    336032 x 6779582   2133.6 per row,  5471.1 MB    310 new,    241 zero   222.741 sec
  14   2256   1875   1144460 x 18963907  3811.9 per row, 33288.2 MB    732 new,   1143 zero  2407.556 sec
  15   5978   5202  error in FGb
Error, (in Groebner:-Basis) Segmentation Violation occurred in external routine

p31:=-2*(a2^3*A20 + a2^2*a3*(2*A20 - A40) + a1^2*(A20*a3 - a3*A30 + a2*(A20 - A40) - a3*A40 + A10*(a3 - a5) - A20*a5) - a4*(A10*a3*(a3 + a4) + A40*a5*(a4 + a5) + A20*(a3 - a5)*(a3 + a4 + a5)) + a1*(A20*a3^2 - a3^2*A30 + 2*a3*A30*a4 + a2^2*(2*A20 - A40) - a3^2*A40 + 2*a3*a4*A40 + 2*a3*A30*a5 + 2*a3*A40*a5 - A20*a5^2 + a2*(2*A10*a3 + 3*A20*a3 - a3*A30 - 2*a3*A40 + 2*a4*A40 - A20*a5) + A10*(a3^2 - a5^2)) - a2*(A40*(a3^2 - 2*a3*a5 - 2*a4*a5) + A20*(-a3^2 + a3*a4 + a4^2 + a4*a5 + a5^2)));

p32:=1/8 + 2*(-(a2^3*A21) + A11*a3^2*a4 + A21*a3^2*a4 + A11*a3*a4^2 + A21*a3*a4^2 - A21*a4^2*a5 + a4^2*A41*a5 - A21*a4*a5^2 + a4*A41*a5^2 - A10*a3^2*b1 - A20*a3^2*b1 + a3^2*A30*b1 - 2*a3*A30*a4*b1 + a3^2*A40*b1 - 2*a3*a4*A40*b1 - 2*a3*A30*a5*b1 - 2*a3*A40*a5*b1 + A10*a5^2*b1 + A20*a5^2*b1 - A20*a3^2*b2 + A20*a3*a4*b2 + A20*a4^2*b2 + a3^2*A40*b2 + A20*a4*a5*b2 - 2*a3*A40*a5*b2 - 2*a4*A40*a5*b2 + A20*a5^2*b2 + 2*A10*a3*a4*b3 + 2*A20*a3*a4*b3 + A10*a4^2*b3 + A20*a4^2*b3 + a2^2*(-2*A21*a3 + a3*A41 - 2*A20*b1 + A40*b1 - 3*A20*b2 - 2*A20*b3 + A40*b3) + A10*a3^2*b4 + A20*a3^2*b4 + 2*A10*a3*a4*b4 + 2*A20*a3*a4*b4 - 2*A20*a4*a5*b4 + 2*a4*A40*a5*b4 - A20*a5^2*b4 + A40*a5^2*b4 - A20*a4^2*b5 + a4^2*A40*b5 - 2*A20*a4*a5*b5 + 2*a4*A40*a5*b5 + a1^2*(-(A21*a3) + a3*A31 + a3*A41 + a2*(-A21 + A41) + A21*a5 + A11*(-a3 + a5) - A20*b2 + A40*b2 - A10*b3 - A20*b3 + A30*b3 + A40*b3 + A10*b5 + A20*b5) + a1*(-(A21*a3^2) + a3^2*A31 - 2*a3*A31*a4 + a3^2*A41 - 2*a3*a4*A41 + a2^2*(-2*A21 + A41) - 2*a3*A31*a5 - 2*a3*A41*a5 + A21*a5^2 + A11*(-a3^2 + a5^2) - 2*A10*a3*b1 - 2*A20*a3*b1 + 2*a3*A30*b1 + 2*a3*A40*b1 + 2*A10*a5*b1 + 2*A20*a5*b1 - 2*A10*a3*b2 - 3*A20*a3*b2 + a3*A30*b2 + 2*a3*A40*b2 - 2*a4*A40*b2 + A20*a5*b2 - 2*A10*a3*b3 - 2*A20*a3*b3 + 2*a3*A30*b3 - 2*A30*a4*b3 + 2*a3*A40*b3 - 2*a4*A40*b3 - 2*A30*a5*b3 - 2*A40*a5*b3 - 2*a3*A30*b4 - 2*a3*A40*b4 - 2*a3*A30*b5 - 2*a3*A40*b5 + 2*A10*a5*b5 + 2*A20*a5*b5 + a2*(-2*A11*a3 - 3*A21*a3 + a3*A31 + 2*a3*A41 - 2*a4*A41 + A21*a5 - 2*A20*b1 + 2*A40*b1 - 4*A20*b2 + 2*A40*b2 - 2*A10*b3 - 3*A20*b3 + A30*b3 + 2*A40*b3 - 2*A40*b4 + A20*b5)) + a2*(a3^2*A41 - 2*a4*A41*a5 + A21*(-a3^2 + a3*a4 + a4^2 + a4*a5 + a5^2) - 2*a4*A40*b1 + A20*a5*b1 + A20*a4*b3 - 2*A40*a5*b3 + 2*A20*a4*b4 + A20*a5*b4 - 2*A40*a5*b4 + A20*a4*b5 - 2*a4*A40*b5 + 2*A20*a5*b5 + a3*(-2*A41*a5 - 2*A10*b1 - 3*A20*b1 + A30*b1 + 2*A40*b1 - 4*A20*b2 + 2*A40*b2 - 2*A20*b3 + 2*A40*b3 + A20*b4 - 2*A40*b5)));

p33:=2*(-(A11*a3^2*b1) - A21*a3^2*b1 + a3^2*A31*b1 - 2*a3*A31*a4*b1 + a3^2*A41*b1 - 2*a3*a4*A41*b1 - 2*a3*A31*a5*b1 - 2*a3*A41*a5*b1 + A11*a5^2*b1 + A21*a5^2*b1 - A10*a3*b1^2 - A20*a3*b1^2 + a3*A30*b1^2 + a3*A40*b1^2 + A10*a5*b1^2 + A20*a5*b1^2 - A21*a3^2*b2 + A21*a3*a4*b2 + A21*a4^2*b2 + a3^2*A41*b2 + A21*a4*a5*b2 - 2*a3*A41*a5*b2 - 2*a4*A41*a5*b2 + A21*a5^2*b2 - 2*A10*a3*b1*b2 - 3*A20*a3*b1*b2 + a3*A30*b1*b2 + 2*a3*A40*b1*b2 - 2*a4*A40*b1*b2 + A20*a5*b1*b2 - 2*A20*a3*b2^2 + a3*A40*b2^2 + 2*A11*a3*a4*b3 + 2*A21*a3*a4*b3 + A11*a4^2*b3 + A21*a4^2*b3 - 2*A10*a3*b1*b3 - 2*A20*a3*b1*b3 + 2*a3*A30*b1*b3 - 2*A30*a4*b1*b3 + 2*a3*A40*b1*b3 - 2*a4*A40*b1*b3 - 2*A30*a5*b1*b3 - 2*A40*a5*b1*b3 - 2*A20*a3*b2*b3 + A20*a4*b2*b3 + 2*a3*A40*b2*b3 - 2*A40*a5*b2*b3 + A10*a4*b3^2 + A20*a4*b3^2 + a2^2*(A41*(b1 + b3) - A21*(2*b1 + 3*b2 + 2*b3)) + A11*a3^2*b4 + A21*a3^2*b4 + 2*A11*a3*a4*b4 + 2*A21*a3*a4*b4 - 2*A21*a4*a5*b4 + 2*a4*A41*a5*b4 - A21*a5^2*b4 + A41*a5^2*b4 - 2*a3*A30*b1*b4 - 2*a3*A40*b1*b4 + A20*a3*b2*b4 + 2*A20*a4*b2*b4 + A20*a5*b2*b4 - 2*A40*a5*b2*b4 + 2*A10*a3*b3*b4 + 2*A20*a3*b3*b4 + 2*A10*a4*b3*b4 + 2*A20*a4*b3*b4 + A10*a3*b4^2 + A20*a3*b4^2 - A20*a5*b4^2 + A40*a5*b4^2 - A21*a4^2*b5 + a4^2*A41*b5 - 2*A21*a4*a5*b5 + 2*a4*A41*a5*b5 - 2*a3*A30*b1*b5 - 2*a3*A40*b1*b5 + 2*A10*a5*b1*b5 + 2*A20*a5*b1*b5 + A20*a4*b2*b5 - 2*a3*A40*b2*b5 - 2*a4*A40*b2*b5 + 2*A20*a5*b2*b5 - 2*A20*a4*b4*b5 + 2*a4*A40*b4*b5 - 2*A20*a5*b4*b5 + 2*A40*a5*b4*b5 - A20*a4*b5^2 + a4*A40*b5^2 + a1^2*(-(A11*b3) + A31*b3 + A41*(b2 + b3) - A21*(b2 + b3 - b5) + A11*b5) + a1*(-2*A21*a3*b1 + 2*a3*A31*b1 + 2*a3*A41*b1 + 2*A21*a5*b1 - 3*A21*a3*b2 + a3*A31*b2 + 2*a3*A41*b2 - 2*a4*A41*b2 + A21*a5*b2 - 2*A20*b1*b2 + 2*A40*b1*b2 - 2*A20*b2^2 + A40*b2^2 - 2*A21*a3*b3 + 2*a3*A31*b3 - 2*A31*a4*b3 + 2*a3*A41*b3 - 2*a4*A41*b3 - 2*A31*a5*b3 - 2*A41*a5*b3 - 2*A10*b1*b3 - 2*A20*b1*b3 + 2*A30*b1*b3 + 2*A40*b1*b3 - 2*A10*b2*b3 - 3*A20*b2*b3 + A30*b2*b3 + 2*A40*b2*b3 - A10*b3^2 - A20*b3^2 + A30*b3^2 + A40*b3^2 - 2*A11*a3*(b1 + b2 + b3) - 2*a3*A31*b4 - 2*a3*A41*b4 - 2*A40*b2*b4 - 2*A30*b3*b4 - 2*A40*b3*b4 - 2*a3*A31*b5 - 2*a3*A41*b5 + 2*A21*a5*b5 + 2*A10*b1*b5 + 2*A20*b1*b5 + A20*b2*b5 - 2*A30*b3*b5 - 2*A40*b3*b5 + A10*b5^2 + A20*b5^2 + 2*A11*a5*(b1 + b5) + a2*((-2*A11 + A31)*b3 + 2*A41*(b1 + b2 + b3 - b4) + A21*(-2*b1 - 4*b2 - 3*b3 + b5))) + a2*(-2*A11*a3*b1 + a3*A31*b1 + 2*a3*A41*b1 - 2*a4*A41*b1 - A20*b1^2 + A40*b1^2 + 2*a3*A41*b2 - 4*A20*b1*b2 + 2*A40*b1*b2 - 3*A20*b2^2 + 2*a3*A41*b3 - 2*A41*a5*b3 - 2*A10*b1*b3 - 3*A20*b1*b3 + A30*b1*b3 + 2*A40*b1*b3 - 4*A20*b2*b3 + 2*A40*b2*b3 - A20*b3^2 + A40*b3^2 - 2*A41*a5*b4 - 2*A40*b1*b4 + A20*b3*b4 + A20*b4^2 - 2*a3*A41*b5 - 2*a4*A41*b5 + A20*b1*b5 - 2*A40*b3*b5 + A20*b4*b5 - 2*A40*b4*b5 + A20*b5^2 + A21*(a3*(-3*b1 - 4*b2 - 2*b3 + b4) + a4*(b3 + 2*b4 + b5) + a5*(b1 + b4 + 2*b5))));

Good day everyone,

I am trying to write various parameters for two functions using "if loop" but it is substituting for the first one only. Anyone with useful information, please.

The link is attached below

Thank you

nops_not_substituting.mw

Is it possible to solve DE without initial conditions
(1/24)*exp(-8)-(1/12)*exp(-5)+(1/24)*exp(-2)-(1/24)*exp(-10)+(1/24)*exp(-9)+(1/24)*exp(-1)+diff(f(x), x, x, x, x, x)+d*(diff(f(x), x))+e*f(x)+a*(diff(f(x), x, x, x, x))+b*(diff(f(x), x, x, x))+c*(diff(f(x), x, x))-1/24

where, a, b, c, d, and e are constant coefficients.....

I would like to have Maple give me sin(2nPi) = 0 assuming that n is a positive integer. Is there a way to do it?

Thank you.
mapleatha.

Dear there,

I have a code.mw

• If I don't use command Digits in the code, I get the following result:

Question 1: The third column of matrix B includes 16 decimal, but the fourth column of matrix B includes 11 decimal. Why?

• When I write the command Digits:=20, I get the following result:

Question 2: The last column of matrix B shows the absolute error of the method. 

When asked what is the absolute error of the method, what is the right answer?  (Because the higher the digit is chosen, the lower the absolute error is.)

Question 3: Are the two results consistent? How can we explain to someone who asks why the difference comes from?

 12 yeas later, the probelm  is not still improved in following links 

https://www.mapleprimes.com/posts/38473-Simplify-Ceil-And-Floor

simplify(ceil(x)+floor(-x));

                         floor(-x) + ceil(x)

I think extending simplify by Joe Riel 8221  is a little complicated. 

restart;
`simplify/ceil` := proc(ex)
    evalindets(ex, 'specfunc(anything,ceil)', x -> -floor(-op(x)));
end proc:

simplify(floor(-x) + ceil(x));

 It seems that maple know  ceil(x)=-floor(-x) 

why does not maple2020 still handle that?  

With each new release of Maple Player, there are more and more restrictions. Tell me, please (in the latest release 2020.1) the ability to copy data from the Maple Player window was removed? (Ctrl+C)? And how do I find out all the restrictions?

How to solve and plot DE?

eq1 := diff(f(x), `$`(x, 5))+2*(diff(f(x), `$`(x, 4)))+diff(f(x), `$`(x, 3))+diff(f(x), `$`(x, 2))+2*(diff(f(x), `$`(x, 1)))+3*f(x) = g(x)

Download pendulumprojection.mw

Most of the time in multivariable calculus the vectors we are decomposing with respect to a given direction are attached to a specific point and this "orthogonal decomposition" should be visualized as a triplet of vectors with initial point at that given point such that the two projections sum to the original vector. Keep in mind our high school physics pendulum example where we need to evaluate both the component of the downward gravitational force along the tangential direction of motion of the pendulum for the equations of motion as well as along the perpendicular direction to the motion to evaluate the tension in the string or wire holding the pendulum mass.

We create an Explorable graphic to visualize this idea and then create an animation which requires a bit of Maple expert user knowledge to accomplish (thanks Maplesoft!). A delayed evaluation of the arrow command from the plot package is required in order to animate that arrow so that it waits for the animation command to feed it actual numerical values for the vector to be plotted.

My worksheet URL:
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2500/handouts/pendulumprojection.mw

Hello all, 

When I enter the following expression:

eqaux_2 := l__bb = L__aa0 + L__aa2 * cos(2*theta - 4/3*Pi);
 

the cos function got converted an equivalent sin function automatically and the result was displayed like this:

l__bb = L__aa0 - L__aa2*sin(2*theta + Pi/6)

Is there any way to ask Maple not to do this automatic conversion?

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/q20210204.mw .
 

Download q20210204.mw
 

This worksheet contains images scanned from a book of problems.

Problem56.mw

Hi,

Suppose I want to create a matrix of derivatives, like gradient, Hessian, or Jacobian, and then apply that matrix to a function.  How do I do this?

Thanks

Hi there,

I'm currently trying to work with combinations where I need to be able to retrieve a list of possible combinations, although i do not actually need to see the output but use it for a later part of programming.

Unfortunately, I get an error message such as the one in the title of this question. 

It seems to me that maple is unable to allocate enough memory to evaluate the problem. I'm not familiar with any way to refine the programming.

are there any possible workarounds for this issue?

Hello,

I was trying to simplify an expression using assume. However, I ended up with very long evaluation time and got an error: "Error, (in type/complex) too many levels of recursion". Here is the case:

Consider the following code:

restart:with(Physics):
simplify(csgn(a-b),assume=[a::real,b::real, a>0,b>0,a>b])

this gives 1 as expected.

However, if I run the following code:

restart:with(Physics):
simplify(csgn(a-b[2]),assume=[a::real,b[2]::real, a>0,b[2]>0,a>b[2]])

I get an error ""Error, (in type/complex) too many levels of recursion" after along evaluation. The last condition a>b[2] is causing the along evaluation time. Without it I get, of course, signum(a-b[2]), which is fine. 

If I do these tests without Physics package loaded, I get the result 1 immediately in both cases without any problem. So, something in Physics package is causing this problem. 

What is the problem? and how can I resolve this issue?

Thank you in advance.