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tomleslie

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15 years, 179 days
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OOps...

tomleslie 13771
December 23 2019
0 0

You wanted the determinant calculated modulo 2, whihc is a "simple" option, as in the attached


 

> 

  restart;
  with(LinearAlgebra):
#
# Generate a (random) 64*64 binary matrix
#
  A:=RandomMatrix(64, 64, generator=rand(0..1)):
  r:=8:
  n := upperbound(A)[1]/r:
  B := Matrix(n, n, 0):
  for i to n do
      for j to n do
          B[i, j] := SubMatrix(A, [(i-1)*r+1 .. i*r], [(j-1)*r+1 .. j*r])
      end do;
  end do;
 
> 

#
# Get the determinants for all the subMatrices in B
#
  Determinant~([entries(B,`nolist`)], method=modular[2]);

[1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]

 (1)
> 

#
# Are any determinants 0?
#
  member(0, %);

true

 (2)
> 

 


 

Download doDets2.mw

Correct...

tomleslie 13771
December 22 2019
0 0

@Carl Love

I don't see a 'Save variables' menu entry anywhere which is why my previous response was titled "A guess"

How I think it works

  1. assuming you have saved as a workbook
  2. you can select multiple variables in the palette ( shift+leftclick)
  3. then rightclick/save on the context menu will save all selected variable assignments

A guess...

tomleslie 13771
December 22 2019
0 0

@Carl Love 

I think the OP might be referring to a context menu entry associated with the variables palette.

AFAIK the 'save' option only "ungreys" if the one's work has been organised/saved as a Maple workbook. It is greyed out for simple worksheets.

It is intended as a means of computing/assignng variables in one worksheet (of a workbook) and having these assignments available in other worksheets (of the same workbook). See the 'Variables Palette' section of ?Workbook Overview

Maple did do the cancellation...

tomleslie 13771
December 21 2019
0 0

@HS 

See the attached

BTW why are you using inert forms of commands eval() and normal() - is this deliberate?

> 

 PS1 := 1;
 PS2 := 10*q;
 QS1 := 8;
 QS2 := 5*q;

1

  

10*q

  

8

  

5*q

 (1)
> 

gP, gQ, S1, S2, P1, P2, Q1, Q2:=
(q*x + 9*q + y)^33*(4*q*x + 6*q + y)^16/((x + 3)^48*(x + 10)), (q*x + 9*q + y)^33*(4*q*x + 6*q + y)^16/((x + 3)^48*(x + 10)), 8, 6*q, 1, q, 1, -10*q    

(q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), (q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), 8, 6*q, 1, q, 1, -10*q

 (2)
> 

#
# OP's original expression - nno idea why (s)he is
# using INERT forms of 'eval' and 'normal'.
#
# The terms Eval(gQ, {x = S1, y = -S2}) in the
# numerator and denominator, should cancel - even
# although the 'Eval' command is inert
#
Normal(Eval(gP, {x = QS1, y = QS2})*Eval(gQ, {x = S1, y = -S2})*1/(Eval(gP, {x = PS1, y = PS2})*Eval(gQ, {x = S1, y = -S2}))) mod p;
#
# Check that the above has performed cancellation correctly
# by doing the cancellation "manually".
#
Normal(Eval(gP, {x = QS1, y = QS2})/(Eval(gP, {x = PS1, y = PS2}))) mod p;

modp(Normal((Eval((q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), {x = 8, y = 5*q}))/(Eval((q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), {x = 1, y = 10*q}))), p)

  

modp(Normal((Eval((q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), {x = 8, y = 5*q}))/(Eval((q*x+9*q+y)^33*(4*q*x+6*q+y)^16/((x+3)^48*(x+10)), {x = 1, y = 10*q}))), p)

 (3)
> 

 


 

Download cancel.mw

You mean...

tomleslie 13771
December 18 2019
0 0

@666 jvbasha 

as in the attached?

You never actually used a "function" definition for f() which would have been (note the syntax)

f:=x->1 - x^2 + c[1]*(-x^3 + x^2) + c[2]*(-x^4 + x^2)

and since such a function definition is not actually required in your worksheet, I just replaced the function f(x), with the name f, everywhere.

> 

restart; with(plots); ha := 15; alp := (1/180)*(5*3.14); rkVals := [5, 10, 15, 20]; f := 1-x^2+c[1]*(-x^3+x^2)+c[2]*(-x^4+x^2); eq1 := diff(f, `$`(x, 3))+2*alp*rk*f*(diff(f, `$`(x, 1)))+(4-ha)*alp^2*(diff(f, `$`(x, 1))); eq2 := collect(expand(eq1), c); a[1] := subs(x = 1/6, eq2); a[2] := subs(x = 2*(1/6), eq2); plts := NULL; colors := [red, green, blue, black]; for j to numelems(rkVals) do rk := rkVals[j]; p := fsolve({a[1], a[2]}); plts := plts, plot(eval(f, p), x = 0 .. 1, color = colors[j]) end do; plots:-display([plts])

 
> 

 


 

Download plotLoop2.mw

It would probably help...

tomleslie 13771
December 18 2019
0 0

if you psoted your complete worksheet using the big green up-arrow in the Mapleprimes toolbar.

From just reading your code, the first loop

for i to 4 do u[i, 1] := sort(collect(expand(-h*(sum(int(K2[i, j]*g[j](t), t = 0 .. x), j = 1 .. 4))), h)) end do

computes the indexed names u[i, 1]. The second loop

for i to 4 do u[i, 2] := sort(collect(expand((1+h)*u[i, 1](x)-h*(sum(int(K2[i, j]*u[j, 1](t), t = 0 .. x), j = 1 .. 4))), h)) end do;

uses these indexed names as if they were functions, ie the terms u[i, 1](x) and u[j, 1](t).

A named (indexed) variable and a named (iindexed) function are two very different things

Please post worksheet...

tomleslie 13771
December 12 2019
0 0

Use the big green up-arrow in the Mapleprimes toolbar to post your worksheet. This makes our life a lot easier

From the information you have supplied, there appear to be multiple undefined quantities - eg sigma, rho, g, h, nu, whihc will have to be given numeric values before fsolve() can be expected to work.

It *may* be better to use the 'complex' option with fsolve() for your problem - see the help at ?fsolve.details

Typo?...

tomleslie 13771
December 10 2019
0 0

@Kitonum 

Shouldn't 'v' be assigned [1, 2, 2] rather than [1, 2, 3] - results in cB=[6, 12, 13]

Observations and simplifications...

tomleslie 13771
December 07 2019
0 0

I have no knowledge of the "Clenshaw derivative" or how it is computed - and I don't plan to read the accompanying documentation to find out. I have "simplified" your code - hopefully without changing the underlying logic.

In your original code there are a few things which don't make much sense. For example, you define Vectors using the initialization

Vector(z..Nm+1+z);

Bad news - the start index for vectors is always 1. To avoid this issue  have redefined these as 1-D arrays, whihc can use any contiguous sange of integers as indexes.

There are a couple of other places (highlighted in the attached) where you rely on the fact that uninitialized quantities will evaluate to zero. This *may* be correct, but the "recursive" nature of the associated calculations means that all values will be determined by these uninitialized quantities. I'd call this seriously high-risk programming

Anyhow, for what it is worth, you might want to check out the attached

> 

  restart:
  Clenshaw_Dx_1D:= proc(z,C,Nm,s)
                        local k,
                              A:= Array(z..Nm+1+z),
                              B:= Array(z..Nm+1+z);
                      #
                      # First iteration of the following loop
                      # both A[k+1] and A[k+2] will evaluate
                      # to zero
                      #
                      # Second iteration of this loop A[k+2] will
                      # evaluate to zero
                      #
                      # This *may* be "desired" behaviour, but just
                      # seems *odd*
                      #
                        for k from Nm-1+z by -1 to 1+z do
                            A[k]:= C[k] + 2*s*A[k+1] - A[k+2]:
                        od:
                      #
                      # First iteration of the following loop
                      # both A[k+1], B[k+1] and B[k+2] will
                      # evaluate to zero
                      #
                      # Second iteration of this loop B[k+2] will
                      # evaluate to zero
                      #
                      # This *may* be "desired" behaviour, but just
                      # seems *odd*
                      #
                        for k from Nm-1+z by -1 to 1+z do
                            B[k]:= 2*A[k+1] + 2*s*B[k+1] - B[k+2]:
                        od:
                        return A[z+1]/2 + s*B[1+z] - B[2+z]:
                   end:

  Chebycoeff1D:= proc(express, Nn, A, B)
                      local C2:= NULL,
                            Cfac:= Array(1..Nn),
                            k, K;
                      for k from 1 to Nn do
                          Cfac[k]:= express( cos(Pi/Nn*(k-0.5))*A+B );
                      od;              
                      for K from 1 to Nn do
                          C2:= C2, (2/Nn)*add
                                          ( Cfac[k]*cos(Pi*(K-1)/Nn*(k-0.5)),
                                            k=1..Nn
                                          );
                      od:
                      return [C2]:
                 end:
> 

  nn:= 1.0:
  Lc:= 0.0:
  Rc:= 1.0:
  xM:= 10: # A guess!
  func:= x -> nn*sin(2*Pi*x)+0.5*nn*sin(Pi*x):
  C:= Array( Chebycoeff1D(func, xM+1, 0.5*(Rc-Lc),0.5*(Rc+Lc))):
  Clen1D_Dx:=Clenshaw_Dx_1D(0, C, xM+1, 0.0);

.9252046157

 (1)
> 

 


 

Download Clen.mw

What attachment??...

tomleslie 13771
December 01 2019
0 0

Use the big green up-arrow in the Mapleprimes toolbar to attach your worksheet

See annotated code attached...

tomleslie 13771
November 27 2019
0 0

BISSEC := proc (P, U, V)\
              #
              # added  packages which this procedure uses
              # so that the latter is "self-contained"
              #
                uses LinearAlgebra, plots;
                local a, b, eq1, eq2, M1, M2, t, PU, PV, bissec1, bissec2;
                a := (P-U)/Norm(P-U, 2)+(P-V)/Norm(P-V, 2);
                M1 := P+a*t;
                b := (P-U)/Norm(P-U, 2)-(P-V)/Norm(P-V, 2);
                M2 := P+b*t;
              #
              # Given M1, M2, defined as above, what is intended
              # by M1[1], M1[2], M2[1], M2[2] in the equations
              # below
              #
                eq1 := op(eliminate({x = M1[1], y = M1[2]}, t));
                eq2 := op(eliminate({x = M2[1], y = M2[2]}, t));
                P := convert(P, list);
                U := convert(U, list);
                V := convert(V, list);
                PU := plot([P, U]);
                PV := plot([P, V]);
                bissec1 := implicitplot(op(eq1[2]), x = 0 .. 5, y = 0 .. 10, color = red);
                bissec2 := implicitplot(op(eq2[2]), x = 0 .. 5, y = 0 .. 10, color = green);
                display([bissec1, bissec2, PU, PV], scaling = constrained)
           end proc:

 

And...

tomleslie 13771
November 23 2019
0 0

@imparter 

what further data do you need????

You say...

tomleslie 13771
November 23 2019
0 0

@imparter 

I want to plot the 2 dimension plot for different values of M . I have three coupled difference scheme .> i am attaching the codes  

Except I have no idea what you want to plot against what!

In the attached, I demonstrate that

  1. In your worksheet you *seem* to generate 270 equations in 272 unknowns.
  2. The unknowns are  C[1..9, 1..10],  T[1..9,1..10], U[1..9,1..10], M, and Gr.
  3. If I provide values for 'M' and 'Gr', this reduces to 270 equations in 270 unknowns - which Maple solves

But what, if anything, should be done with this data????

> 

restart;
# Parameter values:
 Pr:=0.71:E:=1:A:=0:Sc:=0.02: K:=1:

a := 0: b := 1: N := 9:
h := (b-a)/(N+1): k := (b-a)/(N+1):

 lambda:= 1/h^2:  lambda1:= 1/k^2:
# Initial conditions
for i from 0 to N do
  U[i, 0] := h*i+1:
end do:


for i from 0 to N do
  T[i, 0] := h*i+1:
end do:
for i from 0 to N do
  C[i, 0] := h*i+1:
end do:

# Boundary conditions
for j from 0 to N+1 do
  U[0, j] := exp(A*j*lambda);
  U[N+1, j] := 0;
  T[0, j] := j*lambda1;
  T[N+1, j] := 0;
  C[0, j] := j*lambda1;
  C[N+1, j] := 0
end do:


#Discretization Scheme
for i to N do
  for j from 0 to N do
    eq1[i, j]:= lambda1*(U[i, j+1]-U[i, j]) = (Gr/2)*(T[i, j+1]+T[i,j])+(Gr/2)*(C[i, j+1]+C[i,j])+(lambda^2/2)*(U[i-1,j+1]-2*U[i,j+1]+U[i+1,j+1]+U[i-1,j]-2*U[i,j]+U[i+1,j])-(M/2)*(U[i,j+1]+U[i,j]) ;
    eq2[i, j]:= lambda1*(T[i, j+1]-T[i, j]) = (1/Pr)*(lambda^2/2)*(T[i,j+1]-2*T[i,j+1]+T[i+1,j+1]+T[i-1,j]-2*T[i,j]+T[i+1,j])+(E*lambda^2)*((U[i+1,j]-U[i,j])^2);
    eq3[i, j]:= lambda1*(C[i, j+1]-C[i, j]) = (1/Sc)*(lambda^2/2)*(C[i,j+1]-2*C[i,j+1]+C[i+1,j+1]+C[i-1,j]-2*C[i,j]+C[i+1,j])+(K/2)*((C[i,j+1]+C[i,j]))  
  end do
end do:
 
> 

#
# Deeermine the unknowns in the system
#
  `union`(  seq(seq( indets( eq1[i,j], name), i=1..N), j=0..N),
            seq(seq( indets( eq2[i,j], name), i=1..N), j=0..N),
            seq(seq( indets( eq3[i,j], name), i=1..N), j=0..N)
          );
#
# And how many unknowns
#
   numelems(%);
#
# And the number of equations
#
  numelems(eq1)+numelems(eq2)+numelems(eq3);

{Gr, M, C[1, 1], C[1, 2], C[1, 3], C[1, 4], C[1, 5], C[1, 6], C[1, 7], C[1, 8], C[1, 9], C[1, 10], C[2, 1], C[2, 2], C[2, 3], C[2, 4], C[2, 5], C[2, 6], C[2, 7], C[2, 8], C[2, 9], C[2, 10], C[3, 1], C[3, 2], C[3, 3], C[3, 4], C[3, 5], C[3, 6], C[3, 7], C[3, 8], C[3, 9], C[3, 10], C[4, 1], C[4, 2], C[4, 3], C[4, 4], C[4, 5], C[4, 6], C[4, 7], C[4, 8], C[4, 9], C[4, 10], C[5, 1], C[5, 2], C[5, 3], C[5, 4], C[5, 5], C[5, 6], C[5, 7], C[5, 8], C[5, 9], C[5, 10], C[6, 1], C[6, 2], C[6, 3], C[6, 4], C[6, 5], C[6, 6], C[6, 7], C[6, 8], C[6, 9], C[6, 10], C[7, 1], C[7, 2], C[7, 3], C[7, 4], C[7, 5], C[7, 6], C[7, 7], C[7, 8], C[7, 9], C[7, 10], C[8, 1], C[8, 2], C[8, 3], C[8, 4], C[8, 5], C[8, 6], C[8, 7], C[8, 8], C[8, 9], C[8, 10], C[9, 1], C[9, 2], C[9, 3], C[9, 4], C[9, 5], C[9, 6], C[9, 7], C[9, 8], C[9, 9], C[9, 10], T[1, 1], T[1, 2], T[1, 3], T[1, 4], T[1, 5], T[1, 6], T[1, 7], T[1, 8], T[1, 9], T[1, 10], T[2, 1], T[2, 2], T[2, 3], T[2, 4], T[2, 5], T[2, 6], T[2, 7], T[2, 8], T[2, 9], T[2, 10], T[3, 1], T[3, 2], T[3, 3], T[3, 4], T[3, 5], T[3, 6], T[3, 7], T[3, 8], T[3, 9], T[3, 10], T[4, 1], T[4, 2], T[4, 3], T[4, 4], T[4, 5], T[4, 6], T[4, 7], T[4, 8], T[4, 9], T[4, 10], T[5, 1], T[5, 2], T[5, 3], T[5, 4], T[5, 5], T[5, 6], T[5, 7], T[5, 8], T[5, 9], T[5, 10], T[6, 1], T[6, 2], T[6, 3], T[6, 4], T[6, 5], T[6, 6], T[6, 7], T[6, 8], T[6, 9], T[6, 10], T[7, 1], T[7, 2], T[7, 3], T[7, 4], T[7, 5], T[7, 6], T[7, 7], T[7, 8], T[7, 9], T[7, 10], T[8, 1], T[8, 2], T[8, 3], T[8, 4], T[8, 5], T[8, 6], T[8, 7], T[8, 8], T[8, 9], T[8, 10], T[9, 1], T[9, 2], T[9, 3], T[9, 4], T[9, 5], T[9, 6], T[9, 7], T[9, 8], T[9, 9], T[9, 10], U[1, 1], U[1, 2], U[1, 3], U[1, 4], U[1, 5], U[1, 6], U[1, 7], U[1, 8], U[1, 9], U[1, 10], U[2, 1], U[2, 2], U[2, 3], U[2, 4], U[2, 5], U[2, 6], U[2, 7], U[2, 8], U[2, 9], U[2, 10], U[3, 1], U[3, 2], U[3, 3], U[3, 4], U[3, 5], U[3, 6], U[3, 7], U[3, 8], U[3, 9], U[3, 10], U[4, 1], U[4, 2], U[4, 3], U[4, 4], U[4, 5], U[4, 6], U[4, 7], U[4, 8], U[4, 9], U[4, 10], U[5, 1], U[5, 2], U[5, 3], U[5, 4], U[5, 5], U[5, 6], U[5, 7], U[5, 8], U[5, 9], U[5, 10], U[6, 1], U[6, 2], U[6, 3], U[6, 4], U[6, 5], U[6, 6], U[6, 7], U[6, 8], U[6, 9], U[6, 10], U[7, 1], U[7, 2], U[7, 3], U[7, 4], U[7, 5], U[7, 6], U[7, 7], U[7, 8], U[7, 9], U[7, 10], U[8, 1], U[8, 2], U[8, 3], U[8, 4], U[8, 5], U[8, 6], U[8, 7], U[8, 8], U[8, 9], U[8, 10], U[9, 1], U[9, 2], U[9, 3], U[9, 4], U[9, 5], U[9, 6], U[9, 7], U[9, 8], U[9, 9], U[9, 10]}

  

272

  

270

 (1)
> 

#
# So if one supplies values for 'Gr' and 'M', and
# (assuming the equations are consistent), one ought
# to be able to get values for C[1..9, 1..10],
# T[1..9,1..10], and U[1..9,1..10]
#
# As an example below, choos Gr=1.0 and M=2, then the
# following obtains a 'solution` afer a minute or so
#
  fsolve( eval( [ seq(seq(eq1[i,j], i=1..N),j=0..N),
                  seq(seq(eq2[i,j], i=1..N),j=0..N),
                  seq(seq(eq3[i,j], i=1..N),j=0..N)
                ],
                [Gr=1.0, M=2]
              )
        );

{C[1, 1] = -2.987037136, C[1, 2] = 104.9301573, C[1, 3] = 93.04802705, C[1, 4] = 208.8954429, C[1, 5] = 189.0834863, C[1, 6] = 312.8607833, C[1, 7] = 285.1189458, C[1, 8] = 416.8261238, C[1, 9] = 381.1544054, C[1, 10] = 521.7839323, C[2, 1] = -1.988668177, C[2, 2] = .9877141813, C[2, 3] = 101.9154786, C[2, 4] = -6.878246563, C[2, 5] = 213.7438979, C[2, 6] = -22.66763497, C[2, 7] = 333.4958547, C[2, 8] = -46.38056031, C[2, 9] = 461.1713486, C[2, 10] = -77.02415965, C[3, 1] = -1.989942067, C[3, 2] = 1.988549585, C[3, 3] = -2.987634581, C[3, 4] = 106.8486107, C[3, 5] = -115.6688137, C[3, 6] = 331.3105414, C[3, 7] = -355.8688962, C[3, 8] = 691.2085747, C[3, 9] = -739.4222793, C[3, 10] = 1203.370365, C[4, 1] = -1.991256663, C[4, 2] = 1.990181692, C[4, 3] = -1.990419759, C[4, 4] = .9920094061, C[4, 5] = 103.8256555, C[4, 6] = -217.4182788, C[4, 7] = 546.5632778, C[4, 8] = -900.1701899, C[4, 9] = 1588.973464, C[4, 10] = -2324.842817, C[5, 1] = -1.992611984, C[5, 2] = 1.991814992, C[5, 3] = -1.992013193, C[5, 4] = 1.992012631, C[5, 5] = -2.990025164, C[5, 6] = 108.7636006, C[5, 7] = -328.0424876, C[5, 8] = 876.2897633, C[5, 9] = -1777.870973, C[5, 10] = 3368.833309, C[6, 1] = -1.994008043, C[6, 2] = 1.993449504, C[6, 3] = -1.993607935, C[6, 4] = 1.993607549, C[6, 5] = -1.993607676, C[6, 6] = .9959923528, C[6, 7] = 105.7327162, C[6, 8] = -431.6105694, C[6, 9] = 1305.429451, C[6, 10] = -3079.256053, C[7, 1] = -1.995444858, C[7, 2] = 1.995085244, C[7, 3] = -1.995203986, C[7, 4] = 1.995203744, C[7, 5] = -1.995203839, C[7, 6] = 1.995203839, C[7, 7] = -2.992422269, C[7, 8] = 110.6754873, C[7, 9] = -544.0638699, C[7, 10] = 1851.787366, C[8, 1] = -1.996922445, C[8, 2] = 1.996722229, C[8, 3] = -1.996801346, C[8, 4] = 1.996801217, C[8, 5] = -1.996801280, C[8, 6] = 1.996801280, C[8, 7] = -1.996801280, C[8, 8] = .9999795850, C[8, 9] = 107.6366656, C[8, 10] = -648.4507657, C[9, 1] = -1.998440821, C[9, 2] = 1.998360475, C[9, 3] = -1.998400017, C[9, 4] = 1.998399968, C[9, 5] = -1.998400000, C[9, 6] = 1.998400000, C[9, 7] = -1.998400000, C[9, 8] = 1.998400000, C[9, 9] = -2.994825118, C[9, 10] = 113.5799071, T[1, 1] = 2.051943501, T[1, 2] = 97.95738627, T[1, 3] = 103.8443444, T[1, 4] = 194.9704255, T[1, 5] = 207.3004680, T[1, 6] = 290.4890615, T[1, 7] = 312.4331577, T[1, 8] = 384.3165832, T[1, 9] = 419.3874991, T[1, 10] = 477.1327350, T[2, 1] = 3.051261099, T[2, 2] = .3156375825, T[2, 3] = 99.52103631, T[2, 4] = 4.421410864, T[2, 5] = 192.9771636, T[2, 6] = 13.29159212, T[2, 7] = 280.4121624, T[2, 8] = 29.79061451, T[2, 9] = 358.7128970, T[2, 10] = 58.01439391, T[3, 1] = 3.063349007, T[3, 2] = 1.200903643, T[3, 3] = 2.399487524, T[3, 4] = 95.84724691, T[3, 5] = -86.33294602, T[3, 6] = 275.7136622, T[3, 7] = -255.4296074, T[3, 8] = 530.0402551, T[3, 9] = -491.4054127, T[3, 10] = 843.1739982, T[4, 1] = 3.074188563, T[4, 2] = 1.101289867, T[4, 3] = 3.400748677, T[4, 4] = -.9818812947, T[4, 5] = 99.32446116, T[4, 6] = -184.1274183, T[4, 7] = 459.2626794, T[4, 8] = -709.3437173, T[4, 9] = 1233.664839, T[4, 10] = -1713.063713, T[5, 1] = 3.083762040, T[5, 2] = .9831881216, T[5, 3] = 3.451517590, T[5, 4] = -.1477966969, T[5, 5] = 3.082964308, T[5, 6] = 93.70915571, T[5, 7] = -269.2848378, T[5, 8] = 717.2550908, T[5, 9] = -1404.727662, T[5, 10] = 2608.437721, T[6, 1] = 3.092051461, T[6, 2] = .8389149178, T[6, 3] = 3.506547473, T[6, 4] = -.2950015032, T[6, 5] = 4.109573569, T[6, 6] = -2.343669730, T[6, 7] = 99.44920275, T[6, 8] = -366.0630373, T[6, 9] = 1075.035860, T[6, 10] = -2452.732028, T[7, 1] = 3.099038592, T[7, 2] = .6581520192, T[7, 3] = 3.556674117, T[7, 4] = -.5029570870, T[7, 5] = 4.215897147, T[7, 6] = -1.659336274, T[7, 7] = 4.150112060, T[7, 8] = 91.23612469, T[7, 9] = -445.1216297, T[7, 10] = 1496.921080, T[8, 1] = 3.104704940, T[8, 2] = .4269665478, T[8, 3] = 3.583859979, T[8, 4] = -.8146662578, T[8, 5] = 4.308447820, T[8, 6] = -2.026152581, T[8, 7] = 5.214593930, T[8, 8] = -4.179125799, T[8, 9] = 99.92394335, T[8, 10] = -540.9496436, T[9, 1] = 3.109031750, T[9, 2] = .1265218117, T[9, 3] = 3.555703644, T[9, 4] = -1.304792227, T[9, 5] = 4.323309568, T[9, 6] = -2.652987312, T[9, 7] = 5.296816450, T[9, 8] = -4.016085222, T[9, 9] = 5.529854633, T[9, 10] = 88.66581839, U[1, 1] = .8066155842, U[1, 2] = .9462319949, U[1, 3] = .9416200435, U[1, 4] = .9198276005, U[1, 5] = 1.003947662, U[1, 6] = .9387422967, U[1, 7] = 1.038188225, U[1, 8] = .9745224131, U[1, 9] = 1.062854789, U[1, 10] = 1.015991239, U[2, 1] = .6076183125, U[2, 2] = .8810244983, U[2, 3] = .8549869184, U[2, 4] = .8077689863, U[2, 5] = .9618237121, U[2, 6] = .8226672556, U[2, 7] = 1.013487897, U[2, 8] = .8711931233, U[2, 9] = 1.045566943, U[2, 10] = .9316577535, U[3, 1] = .3967886714, U[3, 2] = .8331786289, U[3, 3] = .7305446300, U[3, 4] = .7130097599, U[3, 5] = .8654089652, U[3, 6] = .7187222790, U[3, 7] = .9203879519, U[3, 8] = .7740626852, U[3, 9] = .9456216441, U[3, 10] = .8480115348, U[4, 1] = .1678668208, U[4, 2] = .8119724757, U[4, 3] = .5774625596, U[4, 4] = .6266175580, U[4, 5] = .7639214519, U[4, 6] = .5767309170, U[4, 7] = .8701229573, U[4, 8] = .5705146484, U[4, 9] = .9568269459, U[4, 10] = .5700495724, U[5, 1] = -0.8577241316e-1, U[5, 2] = .8281443464, U[5, 3] = .3821399738, U[5, 4] = .5835477418, U[5, 5] = .6018197140, U[5, 6] = .5117176572, U[5, 7] = .6886090460, U[5, 8] = .5528802846, U[5, 9] = .6688378493, U[5, 10] = .7053786590, U[6, 1] = -.3712533649, U[6, 2] = .8941781292, U[6, 3] = .1278339947, U[6, 4] = .6033522398, U[6, 5] = .3772524594, U[6, 6] = .4873340111, U[6, 7] = .5097288711, U[6, 8] = .4305241541, U[6, 9] = .6470393924, U[6, 10] = .2960555259, U[7, 1] = -.6963434390, U[7, 2] = 1.024841208, U[7, 3] = -.2066582915, U[7, 4] = .7126784925, U[7, 5] = 0.5845611829e-1, U[7, 6] = .5594771709, U[7, 7] = .2145857759, U[7, 8] = .4822840690, U[7, 9] = .2973915372, U[7, 10] = .5229030098, U[8, 1] = -1.069610010, U[8, 2] = 1.237794494, U[8, 3] = -.6483286081, U[8, 4] = .9473653435, U[8, 5] = -.3990023358, U[8, 6] = .7801707953, U[8, 7] = -.2360001550, U[8, 8] = .6746732293, U[8, 9] = -.1177000901, U[8, 10] = .5839162594, U[9, 1] = -1.500593481, U[9, 2] = 1.554293259, U[9, 3] = -1.231550049, U[9, 4] = 1.355300085, U[9, 5] = -1.056875740, U[9, 6] = 1.224710837, U[9, 7] = -.9309659318, U[9, 8] = 1.129739573, U[9, 9] = -.8316431190, U[9, 10] = 1.056090461}

 (2)
> 

 


 

Download bigSys.mw

Not from a plot command...

tomleslie 13771
November 18 2019
0 0

@Stretto 

You can of curse use sommething from the CurveFitting() package to "fit" the data to a model function, or if youu don't know the model function, just use a 'Spline' fit

This time...

tomleslie 13771
November 17 2019
0 0

@Maple_lover1 

with constraints on variables, and checks for "additional" solutions


 

> 

  restart;
> 

  A:=Matrix(2, 2, [[-0.0001633261895*z[1, 2]^2 + 0.0002805135275*z[1, 2]*z[2, 2] - 0.0001200583046*z[2, 2]^2 + 0.0006934805795*z[1, 1]^2 - 0.001190280265*z[1, 1]*z[2, 1] + 0.00007689977894*z[1, 1]*z[1, 2] - 0.00009937418547*z[1, 1]*z[2, 2] + 0.0005090615773*z[2, 1]^2 - 0.00003303758400*z[2, 1]*z[1, 2] + 0.00005683264925*z[2, 1]*z[2, 2] + 0.7021232886*z[1, 1] - 0.3171553245*z[1, 2] - 0.08291569324*z[2, 1] + 0.04647270631*z[2, 2] - 0.1436869545, 0.0002939068385*z[2, 1]^2 + 0.4237544799*z[1, 1] - 0.03129537402*z[1, 2] - 0.06276282411*z[2, 1] + 0.02529757039*z[2, 2] + 0.0004003811990*z[1, 1]^2 + 0.0002177682527*z[1, 1]*z[1, 2] - 0.0006872086309*z[1, 1]*z[2, 1] - 0.0001976167183*z[1, 1]*z[2, 2] - 0.0001764013184*z[2, 1]*z[1, 2] + 0.0001600777394*z[2, 1]*z[2, 2] - 0.1237363898], [0.00006763201108*z[2, 1]*z[1, 2] - 0.0001020812322*z[1, 2]*z[2, 2] - 0.00001554113990*z[2, 1]*z[2, 2] - 0.00003577693711*z[1, 1]*z[1, 2] + 0.0004330743651*z[1, 1]*z[2, 1] - 0.00001941220415*z[1, 1]*z[2, 2] - 0.01736180925 + 0.5623450996*z[2, 1] - 0.2353707048*z[2, 2] - 0.0003226356619*z[1, 1]^2 + 0.00007598605473*z[1, 2]^2 - 0.0001392051452*z[2, 1]^2 + 0.00003283047567*z[2, 2]^2 + 0.04653058230*z[1, 1] - 0.03026711709*z[1, 2], -0.00008037012799*z[2, 1]^2 + 0.03994641178*z[1, 1] - 0.02291248064*z[1, 2] + 0.3140461555*z[2, 1] + 0.01853659924*z[2, 2] - 0.0001862737861*z[1, 1]^2 - 0.0001013147396*z[1, 1]*z[1, 2] + 0.0002500356011*z[1, 1]*z[2, 1] + 0.00005403916772*z[1, 1]*z[2, 2] + 0.00008206914192*z[2, 1]*z[1, 2] - 0.00004377396755*z[2, 1]*z[2, 2] - 0.01370765196]]):
> 

#
# Extract equations from above matrix and define
# constraint ranges for variables
#
  eqs:=[ entries(A, 'nolist') ]:
  rngs:={ seq
          ( j=0..1,
            j in `union`(indets~([entries(A,nolist)])[])
          )
        };

#
# Obtain a solution  of eqs with constraints
#
  sol1:= fsolve( eqs,
                 rngs
               );
#
# Check to see if there are any other solutions
# by telling fsolve() to 'avoid' the one previously
# obtained
#
  sol2:= fsolve(  eqs,
                  rngs,
                  avoid = {sol1}
               );
#
# Double-check by running DirectSearch:-SolveEquations()
# with the 'AllSolutions' option. Just o see if there are
# any other solution, anywhere
#
# OP (probably?) won't be able to do this
#
  DirectSearch:-SolveEquations( eqs,
                                rngs,
                                AllSolutions=true
                              );

rngs := {z[1, 1] = 0 .. 1, z[1, 2] = 0 .. 1, z[2, 1] = 0 .. 1, z[2, 2] = 0 .. 1}

  

sol1 := {z[1, 1] = .3117132485, z[1, 2] = .2328518749, z[2, 1] = 0.2064174947e-1, z[2, 2] = 0.7118281938e-2}

  

sol2 := fsolve([-0.1633261895e-3*z[1, 2]^2+0.2805135275e-3*z[1, 2]*z[2, 2]-0.1200583046e-3*z[2, 2]^2+0.6934805795e-3*z[1, 1]^2-0.1190280265e-2*z[1, 1]*z[2, 1]+0.7689977894e-4*z[1, 1]*z[1, 2]-0.9937418547e-4*z[1, 1]*z[2, 2]+0.5090615773e-3*z[2, 1]^2-0.3303758400e-4*z[2, 1]*z[1, 2]+0.5683264925e-4*z[2, 1]*z[2, 2]+.7021232886*z[1, 1]-.3171553245*z[1, 2]-0.8291569324e-1*z[2, 1]+0.4647270631e-1*z[2, 2]-.1436869545, 0.6763201108e-4*z[2, 1]*z[1, 2]-0.1020812322e-3*z[1, 2]*z[2, 2]-0.1554113990e-4*z[2, 1]*z[2, 2]-0.3577693711e-4*z[1, 1]*z[1, 2]+0.4330743651e-3*z[1, 1]*z[2, 1]-0.1941220415e-4*z[1, 1]*z[2, 2]-0.1736180925e-1+.5623450996*z[2, 1]-.2353707048*z[2, 2]-0.3226356619e-3*z[1, 1]^2+0.7598605473e-4*z[1, 2]^2-0.1392051452e-3*z[2, 1]^2+0.3283047567e-4*z[2, 2]^2+0.4653058230e-1*z[1, 1]-0.3026711709e-1*z[1, 2], 0.2939068385e-3*z[2, 1]^2+.4237544799*z[1, 1]-0.3129537402e-1*z[1, 2]-0.6276282411e-1*z[2, 1]+0.2529757039e-1*z[2, 2]+0.4003811990e-3*z[1, 1]^2+0.2177682527e-3*z[1, 1]*z[1, 2]-0.6872086309e-3*z[1, 1]*z[2, 1]-0.1976167183e-3*z[1, 1]*z[2, 2]-0.1764013184e-3*z[2, 1]*z[1, 2]+0.1600777394e-3*z[2, 1]*z[2, 2]-.1237363898, -0.8037012799e-4*z[2, 1]^2+0.3994641178e-1*z[1, 1]-0.2291248064e-1*z[1, 2]+.3140461555*z[2, 1]+0.1853659924e-1*z[2, 2]-0.1862737861e-3*z[1, 1]^2-0.1013147396e-3*z[1, 1]*z[1, 2]+0.2500356011e-3*z[1, 1]*z[2, 1]+0.5403916772e-4*z[1, 1]*z[2, 2]+0.8206914192e-4*z[2, 1]*z[1, 2]-0.4377396755e-4*z[2, 1]*z[2, 2]-0.1370765196e-1], {z[1, 1], z[1, 2], z[2, 1], z[2, 2]}, {z[1, 1] = 0 .. 1, z[1, 2] = 0 .. 1, z[2, 1] = 0 .. 1, z[2, 2] = 0 .. 1}, avoid = {{z[1, 1] = .3117132485, z[1, 2] = .2328518749, z[2, 1] = 0.2064174947e-1, z[2, 2] = 0.7118281938e-2}})

  

Matrix(%id = 18446744074887932494)

 (1)
> 

#
# Insert solution values into matrix
# in the required order
#
  Z:=Matrix(2,2,(i,j)->eval(z[i,j], sol1 ));

Matrix(2, 2, {(1, 1) = .3117132485, (1, 2) = .2328518749, (2, 1) = 0.2064174947e-1, (2, 2) = 0.7118281938e-2})

 (2)
> 

 


 

Download matSol2.mw

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