resolvent

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12 years, 319 days

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Thank you for your help. I wouldn't know for which command to look under Help.

Now I have the more difficult problem of including multiple if and then statements within my recursion.  My recursion is


with(Physics):

c[i+1,j,k,l] : = (1/((i+1)*d[0]))* sum(iq*d[i+1-iq]*c[iq,j,k,l],iq=1..i) +

sum(c[i-1,j,kq,l]*binomial(i+j-kq-l,k),kq=0..k)

- sum(jq*c[i,jq,k,l]*e[j+1-jq],jq=1..j)

+sum(c[i,j-1,k,l]*binomial(i+j-k-lq,l),lq=0..l)

+KroneckerDelta[i,1]*KroneckerDelta[j,0]*KroneckerDelta[k,0]*KroneckerDelta[l,0]

+KroneckerDelta[i,0]*KroneckerDelta[j,1]*KronckerDelta[k,0]*KroneckerDelta[l,0];

with c[i,j,k,l] = 0 if any of i,j,k,l <0,

c[0,j,k,l] = 0 for all j,k,l if k>0

c[i,0,k,l] = 0 for i,k,l if l>0

and c[0,j,0,l] are assumed known for all j,l and c[i,0,k,0] are assumed known for all i,k and the arrays d[ ] and e[ ] consist of algebraically independent indeterminates.

Hence, I seek to express c[i,j,k,l] in terms of c[0,j',0,l'], c[i',0,k',0], d[0],d[1],...etc e[0],e[1],e[2]...etc

Thank you, acer and Thomas Richard, for filling me in on the details. Not to stray too off-topic: I learn best by formal education: classroom plus stressful, graded, closed-book exams, parts of which include straight memorization. Some things (in life) I have played around a lot with on my own. After all, I never took a typing class in my life nor formal bicycle riding lessons, yet I learned those on my own. However, I find that I need formal classroom training ESPECIALLY for computer programming (as well as human languages, such as French and Russian and Chinese). I simply never can remember the syntax of Java. That has been my personal experience. I'm sure many others share that experience. Even though my C++ professor at a local community college may not have gone into as much detail as my brother wants me to go into, what I learned from my C++ professor in college has stayed with me.  True, I love playing around in the abstract, thinking up / inventing /imagining interfaces and inheritances for classes I'd like to see implemented. But, every time I sit down at a blank Java screen, I can never remember the first things to type on the screen to get anything to work: e.g. the import packages statements.  I spoke and understood more Russian in my classroom at U of Delaware than I did with the Soviets during my summer trip to USSR in 1985.

Naturally, this is why I love Maple (and Mathematica). I can sort of "hit the ground running".  Also, the good thing about speaking foreign HUMAN languages - one can get the "code" only 80% right, and the listener can usually do a decent job of understanding what I MEAN to say and will correct me on the spot. Get only 80% of the code right in a computer language, and one will spend the next YEAR trying to debug the program.

I do admire the whole "object-oriented programming" schema for organizing the world. I really do. It has inspired me to write more math papers, generalizing that schema  - but NOT more computer programs.  But, I've just not found that OOP has helped me get anything PRACTICAL done. (The math-modelling ideas I have which are INSPIRED by OOP will have tremendous practical impact, I believe.)

But, the impracticality of OOP is NOT why I hate Java. I hate Java because of the extreme TYPING of everything. My eyes completely glaze over looking at a Java program, because I literally lose track of whether I am looking at the name of an object or the name of a class/type. Looking at a strongly-typed language such as Java is like reading a book with blurred double-vision.  Also, I cannot keep track of dependencies among classes.

When you say the Standard User Interface, do you mean, for example, the layout of the worksheet (before I enter any Maple commands)?

Thanks. So, to access the Java classes and methods of the Maple Math Library,

should I Google ".mla archives"?

I do not know what the difference between a "compiled" vs an "interpreted" language

means. I'll look that up on wikipedia.

My brother, the expert Java programmer and non-mathematician, admitted to me that he just threw up his hands in digust over this "crazy language"! 2D math seems to confuse (or confuses the user) over issues of displaying data versus manipulating data.
My brother, the expert Java programmer and non-mathematician, admitted to me that he just threw up his hands in digust over this "crazy language"! 2D math seems to confuse (or confuses the user) over issues of displaying data versus manipulating data.
>Compare these two forms, > 10 = 0 mod 5; 10 = 0 > (10 = 0) mod 5; 0 = 0 >In the first of those, the `mod` operator works only on the 0 and not on the 10. When you first pointed this out to me, because I was paying so much attention to the mod operator, I completely failed to notice the far more serious question: what does 10=0 mean? What does 0=0 mean? In C++ and Java, the expression 1==0 evaluates to false. == is a test equality. The symbol = means assignment. Hence, n=0 makes sense. But 1=0 makes no sense. 0=0 makes no sense. In Java and C++, it makes no sense to assign a value to a literal. My brother pointed out that, in fact, in 99.9% of the world's programming languages, a statement like 1=0 or 0=0 (or literal=literal) would have no meaning. Yet, when I type 1=0; in Maple and execute, I get 1=0 in return. Am I missing something here? Should I ask this in a new thread?
>Compare these two forms, > 10 = 0 mod 5; 10 = 0 > (10 = 0) mod 5; 0 = 0 >In the first of those, the `mod` operator works only on the 0 and not on the 10. When you first pointed this out to me, because I was paying so much attention to the mod operator, I completely failed to notice the far more serious question: what does 10=0 mean? What does 0=0 mean? In C++ and Java, the expression 1==0 evaluates to false. == is a test equality. The symbol = means assignment. Hence, n=0 makes sense. But 1=0 makes no sense. 0=0 makes no sense. In Java and C++, it makes no sense to assign a value to a literal. My brother pointed out that, in fact, in 99.9% of the world's programming languages, a statement like 1=0 or 0=0 (or literal=literal) would have no meaning. Yet, when I type 1=0; in Maple and execute, I get 1=0 in return. Am I missing something here? Should I ask this in a new thread?
I really don't think the subtlties of differences in programming languages makes any difference to the struggling programming student - or even the seasoned programming student who still has to climb mountains of new code. The learning individual (which is probably all of us) still has to experiment for themselves, fail, struggle in vain looking in the online help manuals for the correct syntax, fail, and finally ask someone who, just by luck, happened to use the correct code. Maple has thousands of commands. Each individual may use only ten to one hundred of those commands. Collectively, if we're lucky, for any particular command, one individual will know how to use it, or will have used it one time. I often wonder whether anyone really does anything significant with more obscure languages (compared to C++ and Java) such as Prolog, mercury, Godel, Oz. Any time I see a reference to these other computer languages, I see only pedagogical textbook examples that have been done countless times over in other languages.
I really don't think the subtlties of differences in programming languages makes any difference to the struggling programming student - or even the seasoned programming student who still has to climb mountains of new code. The learning individual (which is probably all of us) still has to experiment for themselves, fail, struggle in vain looking in the online help manuals for the correct syntax, fail, and finally ask someone who, just by luck, happened to use the correct code. Maple has thousands of commands. Each individual may use only ten to one hundred of those commands. Collectively, if we're lucky, for any particular command, one individual will know how to use it, or will have used it one time. I often wonder whether anyone really does anything significant with more obscure languages (compared to C++ and Java) such as Prolog, mercury, Godel, Oz. Any time I see a reference to these other computer languages, I see only pedagogical textbook examples that have been done countless times over in other languages.
"Students cannot see the instructor's hands and keyboard to know exactly what was done to enter something that leaves no trace. And, their attention is diverted from the presentation whenever they try something on their own - as they are instructed to do. Miss the wrong step in an interface-based construction and there is no hope of catching up! To me, the interface issues are not solved by creating more tutors and templates. While there is a place for tutors and templates, in the end they boil down to the equivalent of a button on a calculator -- they teach nothing about the mathematics." I have never found software tutorials helpful.
"Students cannot see the instructor's hands and keyboard to know exactly what was done to enter something that leaves no trace. And, their attention is diverted from the presentation whenever they try something on their own - as they are instructed to do. Miss the wrong step in an interface-based construction and there is no hope of catching up! To me, the interface issues are not solved by creating more tutors and templates. While there is a place for tutors and templates, in the end they boil down to the equivalent of a button on a calculator -- they teach nothing about the mathematics." I have never found software tutorials helpful.
After all the effort I put into the last 3 years to force myself to think like a programmer - in terms of a program DOING something - rather than mathematically - in terms of RELATIONSHIPS! I'll stick to math.
After all the effort I put into the last 3 years to force myself to think like a programmer - in terms of a program DOING something - rather than mathematically - in terms of RELATIONSHIPS! I'll stick to math.
I never thought of mod X as a unary operator which RETURNED a value: i.e. 9 mod 5 is 4. I mean, of course, I think that way all the time in MATH, but did not expect that in Maple. I had thought of the mod X as only TESTING equivalence.
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