Mathematica puts everything that they can in the kernel. Every new release more and more of their code is transferred from  Mathematica code to code in C.

SAGE does a similar thing. They are trying to rewrite Python code in Cython, which translates it to C (giving about 30 - 100 times increase in speed usually.)

Alec

Axel,

They have an interesting idea (pointed to me by Alejandro Jakubi) of displaying zero form as 0 times wedge product of the first few differentials. For example,

with(DifferentialGeometry):
DGsetup([x,y,z],M):
dx &wedge dx;

                              0 dx ^ dy

dz &wedge dz;

                              0 dx ^ dy

And it works like that in many cases, except multiplication by 0.

Multiplication by 0 works OK for matrices - it gives a zero matrix instead of 0. I think, it should give a zero differential form here, too, instead of 0.

Alec

Sorry. I don't think you can, unless there is a special package for that which is not a part of the standard Maple distribution - in the Maple Application Center or elsewhere on the web.

Alec

In Calculus, you work with real numbers. In Maple, numbers are complex, and the domain in this example is all complex plane (or, more precisely, the corresponding Riemannian surface, which you might study in further courses.)

Alec

Google translated that as "good eye". What can I say. Citing one of my favorite singers and songwriters, Leonard Cohen (from Tower of Song):

I was born like this, I had no choice
I was born with the gift of a golden voice

Alec

Google translated that as "good eye". What can I say. Citing one of my favorite singers and songwriters, Leonard Cohen (from Tower of Song):

I was born like this, I had no choice
I was born with the gift of a golden voice

Alec

Yes, that's why I used expand. Factoring seems to be either not implemented, or its implementation has a bug.

Same with is - in the factored form it works,

is((1-a)*(1-b)>=0 ) assuming a <= 1, b<=1;

                                 true

Alec

Yes, that's why I used expand. Factoring seems to be either not implemented, or its implementation has a bug.

Same with is - in the factored form it works,

is((1-a)*(1-b)>=0 ) assuming a <= 1, b<=1;

                                 true

Alec

By the way,

solve({expand((1-a)*(1-b))>=0, a<=1});

                           {b = b, a <= 1}

which is wrong, for example, for a=0, b=2

Alec

By the way,

solve({expand((1-a)*(1-b))>=0, a<=1});

                           {b = b, a <= 1}

which is wrong, for example, for a=0, b=2

Alec

It seems as if it should be 1 - and l is not among things desribed at the very beginning.

Alec

It seems as if it should be 1 - and l is not among things desribed at the very beginning.

Alec

The algebraic inequality can be written as

(1-a)*(1-b)+(1-a)*(1-c)+(1-b)*(1-c) >= 0

which is true for a, b, and c less than or equal to 1.

Alec

The algebraic inequality can be written as

(1-a)*(1-b)+(1-a)*(1-c)+(1-b)*(1-c) >= 0

which is true for a, b, and c less than or equal to 1.

Alec

The original example can be done as follows. Start with Nr. Convert cos(a) there to 1-2*sin^2(a/2). Expand. Discard negative terms. Replace cos with 1. The result is 4*Dr.

Alec