# full simplify, sage vs mathematica

I have this somewhat lengthy, but in principal trivial expression

```
sage: B = 1/4*(e^(sqrt(-2*cos(l) + 2)) + 1)*(I*sin(l) -
cos(l))*e^(-1/2*sqrt(-2*cos(l) + 2)) - 1/4*sqrt(-2*cos(l) +
2)*(e^(sqrt(-2*cos(l) + 2))*sin(l)^2/sqrt(-2*cos(l) + 2) +
I*e^(sqrt(-2*cos(l) + 2))*sin(l)*cos(l)/sqrt(-2*cos(l) + 2)
- (I*e^(sqrt(-2*cos(l) + 2)) - I)*sin(l) +
(e^(sqrt(-2*cos(l) + 2)) - 1)*cos(l) - I*e^(sqrt(-2*cos(l) +
2))*sin(l)/sqrt(-2*cos(l) + 2))/(e^(1/2*sqrt(-2*cos(l) +
2))*cos(l) - e^(1/2*sqrt(-2*cos(l) + 2))) +
1/8*sqrt(-2*cos(l) + 2)*((I*e^(sqrt(-2*cos(l) + 2)) -
I)*cos(l) + (e^(sqrt(-2*cos(l) + 2)) - 1)*sin(l) -
I*e^(sqrt(-2*cos(l) + 2)) + I)*(e^(1/2*sqrt(-2*cos(l) +
2))*sin(l)*cos(l)/sqrt(-2*cos(l) + 2) -
2*e^(1/2*sqrt(-2*cos(l) + 2))*sin(l) - e^(1/2*sqrt(-2*cos(l)
+ 2))*sin(l)/sqrt(-2*cos(l) + 2))/(e^(1/2*sqrt(-2*cos(l) +
2))*cos(l) - e^(1/2*sqrt(-2*cos(l) + 2)))^2 -
1/4*((I*e^(sqrt(-2*cos(l) + 2)) - I)*cos(l) +
(e^(sqrt(-2*cos(l) + 2)) - 1)*sin(l) - I*e^(sqrt(-2*cos(l) +
2)) + I)*sin(l)/(sqrt(-2*cos(l) + 2)*(e^(1/2*sqrt(-2*cos(l)
+ 2))*cos(l) - e^(1/2*sqrt(-2*cos(l) + 2))))
```

My humble understanding of full_simply() is, that it will 'kind of' make the 'simplest looking' expression from that.

```
sage: B.full_simply()
1/8*((e^(I*sqrt(cos(l) - 1)*sqrt(2)) + 1)*cos(l)^3 -
3*(e^(I*sqrt(cos(l) - 1)*sqrt(2)) + 1)*cos(l)^2 +
3*(e^(I*sqrt(cos(l) - 1)*sqrt(2)) + 1)*cos(l) +
((-I*e^(I*sqrt(cos(l) - 1)*sqrt(2)) - I)*cos(l)^2 +
(2*I*e^(I*sqrt(cos(l) - 1)*sqrt(2)) + 2*I)*cos(l) -
I*e^(I*sqrt(cos(l) - 1)*sqrt(2)) - I)*sin(l) + sqrt(cos(l) -
1)*((I*sqrt(2)*e^(I*sqrt(cos(l) - 1)*sqrt(2)) -
I*sqrt(2))*cos(l)^2 + (-2*I*sqrt(2)*e^(I*sqrt(cos(l) -
1)*sqrt(2)) + 2*I*sqrt(2))*cos(l) +
((sqrt(2)*e^(I*sqrt(cos(l) - 1)*sqrt(2)) - sqrt(2))*cos(l) -
sqrt(2)*e^(I*sqrt(cos(l) - 1)*sqrt(2)) + sqrt(2))*sin(l) +
I*sqrt(2)*e^(I*sqrt(cos(l) - 1)*sqrt(2)) - I*sqrt(2)) -
e^(I*sqrt(cos(l) - 1)*sqrt(2)) - 1)/(e^(1/2*I*sqrt(cos(l) -
1)*sqrt(2))*sin(l)^2 + 2*e^(1/2*I*sqrt(cos(l) -
1)*sqrt(2))*cos(l) - 2*e^(1/2*I*sqrt(cos(l) - 1)*sqrt(2)))
```

That doesn ...

Is it really fully_simply?

@G-Sage TAB completion produces both, full_simplify() and simplify_full() and they both return the same results - moreover the doc says: simplify_full(...) File: sage/symbolic/expression.pyx (starting at line 6553) Applies simplify_factorial, simplify_trig, simplify_rational, simplify_radical, simplify_log, and again simplify_rational to self (in that order). ALIAS: simplify_full and full_simplify are the same

What is `l` here? A symbolic variable?

I don't know that an "answer" is really appropriate here. It's pretty well-known among power users that symbolic manipulation is something that Maple and Mma do better than Maxima (which provides our simplification). It's unfortunate, but that is one reason we provide the hooks to other programs.

@Xaver First, I had a slight typo (extra y), but my question was is it really full_simply? You responded by saying there exists full_simplify. These are different. It's not that important. I just thought it was weird to have full_simply when it's so close to the full phrase.