consider quadratic equation ax^2+bx+c =0 :
the coefficients vary between -1 and +1 . just like this :
-1<a<+1 , -1<b<+1 , -1<c<+1 ;
how can some one proove that this equation should have real answers ?! can anybody help ? thanks in advance.

i am very new with Maple.

I have the following two equations:

x1=a-y1-d*y2;

x2=a-y2-d*y1;

I wish to express the first equation in terms of y1 and x2, so that

x1 = c - b*y1+d*x2;

where c=a-a*d and b=1-d^2. How can I get maple to rearrange the original equation x1 in term of y1, x2, c and b? 

This question is probably for maple devs...

I was wondering if it would be possible to outline what algorithm is used to generate replications (realizations) for various processes by the Finance:-SamplePath command (and friends). For example in the code like this:

with(Finance):

X := WienerProcess();
A := SamplePath(X(t), t = 0 .. 1, timesteps = 100, replications = 20);

Is it the Euler-Maruyama method?

Alternatively maybe you can show the portion of the code that is responsible for the integration of the SDE that the Wiener process defines.

I can't find any details related to this information in the help, and it would be very helpful to know this (and more importantly have it in the help section).

Thanks!

Hi,

     I was wondering if there is an easy way to define another set of indices in the Physics package. For example, usually greek indices are for all 4 spacetime dimensions. Using Setup(spaceindices = lowercaselatin), we can define 3 of those as space indices. I was hoping there is a more general command, so that I could use only 2 indices as "space indices". For example, X[i] would run over x,y while X[mu] would run over t, z. Is there such a command in the Physics package, or a simple way to implement this personally?

Second thing. I was playing with SumOverRepeatedIndices on an expression that contained both space indices and spacetime indices. Usually this seems to work, but in my attached example it does not. I tried the same thing with just spacetime indices in Maple 18 (newest Physics update) and it gave the same error.

Any help appreciated,

PhysicsBug.mw

Is there a way to make the first part of this look like the second picture depicted here? Also after intigration is there a way to make the highlighted posrtion not have an "ln(e)" parts and just have the exponetials and there constants?

Obviously I dont want to have to manually input this section everytime, is there some command I can use to achieve this goal?

I'm trying to determine that f(x) = (a/2)*e^(-a|x|) is a pdf for which I have tried to calcuate the integral from -infinity to +infinity but I am no getting a result that converges(even the wolfram alpha widget said the integral doesn't converge). How do I correcly implement this?

Above is the outcome I am getting at the current time... and I used map(expand,...) to do the expansion then simplifing it goes back to the origional. 

Below is the outcome I would like to achieve...you can see that this is a different method. The problem I have is this is the right click method of expansion and I am tring to build a program that solves matrix ODE's by just inputing the initial matrix and it doing everything so i can check my answers step by step. 

So my question is, is there another method of command input to get the bottom line in the below picture?

convert(Matrix(2, 2, {(1, 1) = (s-2)/(s^2-s-12), (1, 2) = -5/(s^2-s-12), (2, 1) = -2/(s^2-s-12), (2, 2) = (s+1)/(s^2-s-12)}), parfrac);
%;
Error, (in convert/parfrac) input must be a rational polynomial in s

gives me that error and i assume I can not use this command for matrix opperations if that is true is there a way to do it such as issolateing each element and doing each individually and putting it back into a matrix is that posible if so can someone show me the code for that?

I know 1st root of a function locates in a small interval (by drawing plots of function).

but fsolve command uses unreasonable time to find roots.

Also NextZero dosent work.

Please help me.

Thanks for your attention.

--------------------------------------------------------------------------------------------------

restart; s := sqrt(n)*Pi*(sqrt(n)*Pi-tan(sqrt(n)*Pi))/(sqrt(n)*Pi*tan(sqrt(n)*Pi)+2*(1-sec(sqrt(n)*Pi)));

C := (tan(sqrt(n)*Pi)-sqrt(n)*Pi*sec(sqrt(n)*Pi))/(sqrt(n)*Pi-tan(sqrt(n)*Pi));

S := s*(-C^2+1);

Gamma[b] := E[b2]/E[b1];

Gamma[c] := E[c2]/E[c1];

alpha[b] := t[b1]*t[b2]/(t[b1]+t[b2])^2;

alpha[c] := t[c1]*t[c2]/(t[c1]+t[c2])^2;

EIb := b*E[b1]*(t[b1]^4+2*Gamma[b]*alpha[b]*(2-alpha[b])*(t[b1]+t[b2])^4+Gamma[b]^2*t[b2]^4)/(12*(Gamma[b]*t[b2]+t[b1]));

EIc := b*E[c1]*(t[c1]^4+2*Gamma[c]*alpha[c]*(2-alpha[c])*(t[c1]+t[c2])^4+Gamma[c]^2*t[c2]^4)/(12*(Gamma[c]*t[c2]+t[c1]));

b := 1;Lb := 2; Lc1 := 2.5; Lc2 := 3; E[b1] := 180; E[b2] := 200; t[b1] := 0.3e-1; t[b2] := 0.4e-1; E[c2] := 220; t[c1] := 0.5e-1; t[c2] := 0.2e-1;

for k from 0 by 10 to 100 do

E[c1] := 150+k; nce := (1/2)*(Lc1/Lc2)^2*n; nb := (1/2)*(Lb/Lc2)^2*n; q[k] := 1000*fsolve((subs(n = nce, C*s)*EIc/Lc1)^2/(S*EIc/Lc2+subs(n = nce, s)*EIc/Lc1+subs(n = nb, s*(1-C))*EIb/Lb)-subs(n = nce, s)*EIc/Lc1-2*EIb/Lb, n = 1.45 .. 1.56)*evalf(Pi^2)*EIc/(2*Lc2^2); print(q[k], k)

end do;

with(CurveFitting); F := PolynomialInterpolation([seq([10*i, q[10*i]], i = 0 .. 10)], z)

Trying to get this function to work in Maple 18 

CharacteristicPolynomial(M,x)

I am trying to creat a way to solve matrix differential equations step by step.

Hello Forum:

In the Programming Guide, section 14.3 (Programming Guide: Advanced Connectivity), the subsection `Runtime Environment Prerequisites' a sample script is given in order to set up the environment varibales MAPLE and LD_LIBRARY_PATH:

--8><--------------------------------------------------------------------------

#!/bin/sh
export MAPLE="/usr/local/maple"
. $MAPLE/bin/maple -norun
myapp $*

-----------------------------------------------------------------><8-----------

For testing, `my app $*' can be replaced by `printenv': it seems not to work with Maple 2015.

Any hint ?

Thanks in advance,

Jerome

hi.please help me .why rule ''''Det'''' dose not work properly?

this program attached DET.mwblow.thanks alot

hi.please help me .why rule ''''evalf'''' dose not work properly?and I should copy the former answer in a another 'evalf' rule a gain??can I use only one rule 'evalf' instad twice useage??

this program attached blow.thanks alot

evalf.mw

Hi, I am trying to figure out how to find the maxima and minima of the function f(x)=(x^3-10*x^2-2*x+1)/(4*x^3+5*x+1) and its derivative.

a) Find the local maxima and minima of f. 

b) Find the vertical asymptote

I graphed the function and located the  local max to be (-1,1) and local min (1,-1) however, I can't figure out how to plot the derivative of the function. I tried to use the diff expression but it leaves the graph empty when i attempt to plot it.

Also, just curious how am i able to join text words and maple commands together? For example, I want to be able to say "The derivative of the original function is [maple command here]" ? I tried to switch from text to math however nothing worked.

Thanks in advance!

I want to find numerically the limit lim(y[m](t),m = infinity), do you have an idea how to do implement it in maple?

Download recursive_integral.mw