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Addition of matrix and scalar...

Asked by: John Fredsted 2253
matrix linear-algebra addition
January 20 2014
1  4

The following code

restart:
A := Matrix(2,(i,j) -> a||i||j):
A + 1;
A + a;

produces the following output:

Why does Maple accept these additions, which mathematically are nonsensical? And why, if accepting these mathematically, does Maple not evaluate them analogously by putting the scalars either inside or outside the matrix in both cases?

implicit keller box scheme...

Asked by: platonian 5
homework pde numeric
January 19 2014
1  0

Hello;
        i am wording on fluid dynamics, in which i can up a system of nonlinear partial differential equation with i am suppose to solve using implicit keller box method. i need an asistance on how to implement this in maple.

how to correctly stop maple in c# after call...

Asked by: LeeHoYeung 535
module
January 19 2014
0  0

 

error module is maple.dll_unloaded

 

i have already called stopmaple(kv);

in

testfunction(string hello){....stopmaple(kv));

 

testfunction(1);

testfunction(2);

when call testfunction again , it got error

Has anyone written Maple code for quaternions or d...

Asked by: spradlig 70
January 18 2014
1  3

Maple people:

The title is the question.  I would like to know if there is any Maple code available, either part of Maple itself or written by a user, to do computations with quaternions or dual quaternions.

I could Google this and probably find something, but I'll probably find a more helpful and less outdated answer here.

I am teaching a student about the subject and I'd like something to help me teach and help him learn.

I have a lot of experience with Maple but I am not a "computer person", so if the code involves fancy "libraries" or something beyond regular Maple worksheets, I may need a few tips how to use it.

GS

In the Palettes Expressions, how to add a input pl...

Asked by: lemelinm 1545
January 18 2014
0  0

Hello everybody,

 

This one is an easy one but I cannot find the answers.  Suppose that I clik on the template for evaluating a function.  But mine have two (or more) variables (f=f(x,y)).  I have the x=a as one placeholder.  But I need to have an another inplut placeholder for y=b.  Can somenone tell me how to do it under Windows and under Linux.

 

Thank you in advance for your help.

 

--------------------------------------
Mario Lemelin
Maple 17 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

how to change this into algebra...

Asked by: LeeHoYeung 535
algebra
January 17 2014
1  5

ifactor(op(1, convert(0.999987406876435, fraction)));
ifactor(op(2, convert(0.999987406876435, fraction)));

ifactor(op(1, convert(0.999919848203811, fraction)));
ifactor(op(2, convert(0.999919848203811, fraction)));

x1:=2;
x2:=3;
x3:=7;
x4:=17;
x5:=173;
x6:=709;
x7:=5347;
x8:=18713;

i think that there is a need to distinct all factor into a list of x1,x2,x3.... depending on all factors in these two decimal

0.999987406876435 = x4*x2^3*x5/(x3*x1^4*x6)
0.999919848203811 = x1*x8/(x3*x7);

then replace factors with x1,x2,x3....

how to basis this...

Asked by: LeeHoYeung 535
groebner
January 17 2014
0  1

with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3],[e1,e2,e3]);
GB := Basis([e1+.999987406876435, e2-.999919848203811],T):

Error, (in LinearAlgebra:-Basis) invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, {set(Vector), list(Vector)}} but received [e1+HFloat(0.9999874068764352), e2-HFloat(0.9999198482038109)]


with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3,x4,x5,x6,x7,x8],[e1,e2]);
GB := Basis([e1-x4*x2^3*x5/(x3*x1^4*x6), e2-x1*x8/(x3*x7)],T):

Error, (in LinearAlgebra:-Basis) invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, {set(Vector), list(Vector)}} but received [e1-x4*x2^3*x5/(x3*x1^4*x6), e2-x1*x8/(x3*x7)]

How do I solve a equal degree splitting problem...

Asked by: candy898 60
polynomial
January 17 2014
0  5
u_{tt} = c^2 u_{xx}, \,
u(t,0)=0, \quad u(t,L)=0,

as well as the initial conditions

u(0,x)=f(x), \quad u_t(0,x)=g(x).

 

how do I solve a distinct-degree decomposition pro...

Asked by: candy898 60
January 17 2014
0  1

Trace  on computing the distinct-degree decomposition of the squarefree polynomial
f=x^17+2x^15+4x^13+x^12+2x^11+2x^10+3x^9+4x^4+3x^3+2x^2+4x belong to F_5[x].tell from the output only how many irreducible factors of degree i the polynomial f has, for all i.

 

Calculating Integrals via different ways...

Asked by: digerdiga 390
integration
January 17 2014
1  1

Mapleprimes_Integral.mw

I have a question regarding following problem:

assume(a > 0, a < 1, t > 0, Z0 > 0, z > 0)

f1 := proc (z) options operator, arrow; 1/z end proc

proc (z) options operator, arrow; 1/z end proc

 (1)

I_1 := int(f1(z)*ln((a*z+1)/(1+z/a)), z = 0 .. Z0); 1; MultiSeries:-asympt(%, Z0, 3)

2*ln(Z0)*ln(a)+(a^2-1)/(a*Z0)-(1/4)*(a^4-1)/(a^2*Z0^2)+O(1/Z0^3)

 (2)

Using the representation which should hold for all a>0 and z>0

int(z*exp(t)*(a^2-1)/((exp(t)+a*z)*(exp(t)*a+z)), t = 0 .. infinity); 1; combine(%)

ln((a*z+1)*a/(z+a))

 (3)

I'm calculating the result the other way around

int(z*exp(t)*(a^2-1)*f1(z)/((exp(t)+a*z)*(exp(t)*a+z)), z = 0 .. Z0); 1; I_2 := int(%, t = 0 .. infinity); 1; MultiSeries:-asympt(%, Z0, 3)

2*ln(Z0)*ln(a)+(a^2-1)/(a*Z0)-(1/4)*(a^4-1)/(a^2*Z0^2)+O(1/Z0^3)

 (4)

plot(eval([I_1, I_2], a = 1/2), Z0 = 0 .. 10)

  

So the results are the same.

But if I calculate this with another function

f2 := proc (z) options operator, arrow; 1/(z*(z+a)) end proc

proc (z) options operator, arrow; 1/(z*(z+a)) end proc

 (5)

I_3 := int(f2(z)*ln((a*z+1)/(1+z/a)), z = 0 .. Z0); 1; MultiSeries:-asympt(%, Z0, 3)

-dilog(a^2)/a-2*ln(a)/Z0+(1/2)*(2*ln(a)*a^2+a^2-1)/(a*Z0^2)+O(1/Z0^3)

 (6)

int(z*exp(t)*(a^2-1)*f2(z)/((exp(t)+z*a)*(exp(t)*a+z)), z = 0 .. Z0); 1; I_4 := IntegrationTools:-Change(int(%, t = 0 .. infinity), t = ln(z)); 1; MultiSeries:-asympt(%, Z0, 3); 1; simplify(convert(convert(MultiSeries:-series(I_4, Z0, 1), polynom), polynom))

ln(a)*(ln(Z0)+ln(a))/a

 (7)

I get another result :-/ The Integral doesn't even vanish in the limit Z0 -> 0

Though if I take the limit prior:

int(z*exp(t)*(a^2-1)*f2(z)/((exp(t)+z*a)*(exp(t)*a+z)), z = 0 .. infinity);

-dilog(a^2)/a

 (8)

the result is correct. What is the problem here?



Download Mapleprimes_Integral.mw

 

Real roots only...

Asked by: Syeda 30
real roots
January 17 2014
0  2

I want to find real roots only.  Cannot we find a simplified formula for x in this case which gives only real roots? 

 

 

``

eq1 := a^2*x^3+Typesetting:-delayDotProduct(2*a*b-Typesetting:-delayDotProduct(a^2, e), x^2)+(-2*a*b*c^2-a*c+b^2)*x-c*b-d-b^2*e = 0:

``

# Formula

eq2 := A*x^3+B*x^2+C*x+E = 0:

``

NULL

a := .7438:

b := 15.12*z[1]+10.85*z[1]^2:

c := 18.92-17.76*z[2]:

d := -.9224:

e := 2.106-5.317*z[2]+2.87*z[2]^2:NULL

NULL

A := a^2:

B := -a^2*e+2*a*b:

C := -2*a*b*e^2-a*c+b^2:

E := -b^2*e-b*c-d:

``

eq2

.55323844*x^3+(-1.165120155+2.941568785*z[2]-1.587794323*z[2]^2+22.492512*z[1]+16.140460*z[1]^2)*x^2+(-1.4876*(15.12*z[1]+10.85*z[1]^2)*(2.106-5.317*z[2]+2.87*z[2]^2)^2-14.072696+13.209888*z[2]+(15.12*z[1]+10.85*z[1]^2)^2)*x-(15.12*z[1]+10.85*z[1]^2)^2*(2.106-5.317*z[2]+2.87*z[2]^2)-(15.12*z[1]+10.85*z[1]^2)*(18.92-17.76*z[2])+.9224 = 0

 (1)

``

``# Putting z1 and z2 value

"(->)"

.55323844*x^3+14.11629660*x^2+83.26002702*x-3.52866181 = 0

 (2)

 

"(->)"

[[x = 0.4208050385e-1], [x = -9.354079555], [x = -16.20375615]]

 (3)

``

``

 

Download cubic.mw

Sort alpha list...

Asked by: brian bovril 914
January 17 2014
2  11

Gentlemen

I know the following:{A>E,F>Z,F<P,Z>E,P<A} , all real Numbers

can I get maple to sort these in order largest to smallest.

[in this case:  A>P>F>Z>E ]

How to convert "sin(x)+cos(x)" into "sqrt(2)*sin(x...

Asked by: lcrpn 20
January 17 2014
2  7

As the title, how to convert "sin(x)+cos(x)" and this kinds into "sqrt(2)*sin(x+pi/4)"?

Sum of two sine functions with the same cycle should can be converted into one sine function, with some amplitude gain and phase offset. 

 

Error, attempting to assign to "D" which is protec...

Asked by: Syeda 30
student warning
January 17 2014
0  4

While solving cubic formula, i got this warning in Maple.

Why D variable is protected? 

eq1 := A*x^3+B*x^2+C*x+D = 0

``

A := x^2:

B := 2*x*y-4*z^2:

C := -2*x*y*z+x^2-y*z:

D := 4*x^2-x*z

Error, attempting to assign to `D` which is protected.  Try declaring `local D`; see ?protect for details.

  

``

eq1

x^5+(2*x*y-4*z^2)*x^2+(-2*x*y*z+x^2-y*z)*x+D = 0

 (1)

 

 

Joining points on a graph...

Asked by: abbeykabir 85
January 16 2014
1  4

How can I join the points on this graph to look like the second graph below.

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