How do I locate a particular theorem in Linear Algebra that I need for my research?
I have been to conferences which seriously discussed a unified and universal bank of all known math theorems. Theoretically, all proven math theorems could be connected logically: A implies B. But, in reality, most proven math theorems are scattered throughout the literature.
I have no access to a university with math journals.
I might be able to do inter-library loan at my local community county college here in the United States. But, that may take a long time. I have no paid job. My earned income is only from social security disability.
I noticed that when using Maple my %CPU seems to be much higher than other apps. This is not just during computation. I may just be entering text, but once I have executed any commands in the worksheet or document the percent seems to stay between 50 and 70. I can stop entering anything for several minutes and it just stays at this level. As soon as I click outside the worksheet on the desktop or on another app it immediately drops down to practically nothing. If I then click back on the worksheet it stays down until I start to enter something and then it jumps back up.
Is this typical? It gets things heated up pretty quickly and as far as I can tell it is my only app that does this.
We're running Maple 11 in a lab of about 40 MiniMacs (MacOS X).
Normally, there is a Preferences choice under Maple 11 on the menu. But one student had no Preferences there (or anywhere else that I could find: in particular, not under Tools, where Options would be under Windows). What's going on?
I occasionally use e.g. expr := 1+a^2; eval( expr, 2=-1 ); to convert expr to 1+1/a.
I realised recently that this can be dangerous: expr2 := 1+x+3*y; eval(expr2, 1=2); produces (rather suprisingly) 4+2x+3y.
Investigating, pulling apart expr2 with op reveals the structure as being a sum of 3 terms, the last being a product. "ToInert" shows essentially the same. "dismantle" however shows expr 2 as being a single sum of the form 1.1 + 1.x + 3.y.
So it is essentially the dismantle version that eval searches and replaces all the 1's by 2's.
My question is whether there is some good reason for this. It would seem to me (without knowing much about the theory of computer algebra) that eval (and subs) should work on the operands as revealed by op or ToInert. Certainly it would lead to more logical results in cases like my example.
I was solving a task in flow through a pipe and noticed a result from int where floats were changed into a RootOf containing integers and fractions. I was surprised by the result. Here is a very simple example:
f:=z->solve(y/(1.+(-0.5*y)^0.8)=z,y);
v:=x->int(f,-10..x);
v(-1);
Is it common for Maple to change floats into integers and fractions for symbolic analysis? It seems to violate the rules.
Thanks,
Lee
View 4238_Odd Solve Example.mw on MapleNet or
What is the canonical (and therefore also safe) way to pull out a specific argument of a function contained in the nested output from ToInert?
I ask because it seems that using something like op(n1...,op(nk,ToInert(expr))...), where n1...nk are positive integers, is a bad idea because the arguments can change locations depending on the exact expression being translated to inert form. For instance, inserting a specific shape in the Matrix constructor changes locations of all the other arguments of _Inert_MATRIX.
Is it using iteratively something along the following lines?
Is there a size limit on the matrices and vectors?
In case there is one, is it possible to extend this limitation?
I've done a proc to produce a list of compound Poisson random variables as below, but it's not fast enough. I suspect there are better ways to do the same. Comments and solutions welcome!
with(Statistics):
FFFF := proc (g)
local i, x, y, S;
for i to g do x[i] := floor(convert(Sample(RandomVariable(Poisson(1)), 1), `+`));
if 0
Recently Dr. Israel responded to my request for help in extending the EllipticF function past the limit of Pi/2 for the amplitude (see topic titled Elliptic Integrals). After reviewing A&S Chapter 17, I have tried to duplicate the results using the JacobiAM function in Maple. The help page for this function indicates that there is no limit on the amplitude. The attached worksheet evaluates the form suggested by A&S, Eq. 17.4.3 and the JacobiAM function. It is interesting to note the only when the argument given to the EllipticF function is equal to the remainder of Pi/2 - beta that the two expressions are equal. I would think that the JacobiAM form is a more compact representation of EllipticF for amplitudes greater than Pi/2. Are the two functions equivalent as used in the worksheet?
Hello people.
I tried to plot the graph
plot(sqrt(sin(x))/sqrt(cos(x)))
and I believe it was wrong.
The graph was different from the one my Ti gave.
So I went online and check with a third party online grapher:
http://www.walterzorn.com/grapher/grapher_e.htm
and do some calculation on my own. I believe Maple's was wrong.
Any idea? Thanks.
Hi there.
How are you?
I feel sorry since I purchased Maple. Let see if you would agree.
First of all, it is inferior to the Ti-89 in some aspects.
I have tried to use Maple 11.02 to solve the problems:
(sqrt(2)+1)^x+(sqrt(2)-1)^x = 3;
And Maple 11.02 fail to solve, then I tried to solve numerically, it missed one solution.
There must be 2 solutions for the problem above and Maple missed 1, the Ti-89 beats it hand down.
The second problem I tried was:
int(sqrt(sin(x))/(sqrt(sin(x))+sqrt(cos(x))), x = 0 .. (1/2)*Pi);
and Maple even stuck... The Ti-89 return answer correctly within about 20 secs.
This week I made up an exam using Maple where I didn't want the input to be visible. I used View|Show/Hide to accomplish that. This worked alright within a short time frame. I could save the file with the input hidden, and then I could reload the file and, upon re-checking input to show, all the input would re-appear. However, when I let the file sit for a few days and then tried to re-show the input today, all the input in each execution group was condensed into one line with '?'.
This sure seems like a Maple bug to me. Does anyone have any other ideas about how this could happen? Or how one might recover the input?
I am fooling around a bit with
dismantle and
ToInert. In the light of the passage "For the exact internal representation, see dismantle," in the help page on
ToInert, I am surprised to see that
dismantle does not provide any information concerning the entries of a given matrix, as do
ToInert:
expr := Matrix(2,2,(i,j) -> m||i||j):
dismantle(expr);
ToInert(expr);
RTABLE(11): 4 [1..2, 1..2]
NAME(6): anything #[protected]
_Inert_MATRIX(_Inert_RANGE(_Inert_INTPOS(1), _Inert_INTPOS(2)), _Inert_RANGE(_Inert_INTPOS(1), _Inert_INTPOS(2)), _Inert_SET(_Inert_EXPSEQ(_Inert_EQUATION(_Inert_EXPSEQ(_Inert_INTPOS(1), _Inert_INTPOS(1)), _Inert_NAME("m11")), _Inert_EQUATION(_Inert_EXPSEQ(_Inert_INTPOS(1), _Inert_INTPOS(2)), _Inert_NAME("m12")), _Inert_EQUATION(_Inert_EXPSEQ(_Inert_INTPOS(2), _Inert_INTPOS(1)), _Inert_NAME("m21")), _Inert_EQUATION(_Inert_EXPSEQ(_Inert_INTPOS(2), _Inert_INTPOS(2)), _Inert_NAME("m22")))), _Inert_EQUATION(_Inert_NAME("datatype"), _Inert_NAME("anything", _Inert_ATTRIBUTE(_Inert_NAME("protected", _Inert_ATTRIBUTE(_Inert_NAME("protected")))))), _Inert_EQUATION(_Inert_NAME("storage"), _Inert_NAME("rectangular")), _Inert_EQUATION(_Inert_ASSIGNEDNAME("order", "PROC", _Inert_ATTRIBUTE(_Inert_NAME("protected", _Inert_ATTRIBUTE(_Inert_NAME("protected"))))), _Inert_NAME("Fortran_order")))
Why am I getting this strange result?
evalb(sin(1)/cos(1) - tan(1) = 0) gives false
but
evalf(sin(1)/cos(1) - tan(1)) gives 0
so the evalb should give true.
I originally got a result of
(sin(x)^3) / (cos(x)^3)
in a calculation and asked maple to simplify, expecting tan(x)^3. This led to my investigation of my assumptions about this trig identity. However, for the specific example above, Maple seems to be flat out wrong. Also the boolean returns true if the arg is changed to 0.
