Add half-angle transformations

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

In some circumstances (e.g. integration), it may be useful to rewrite

• expressions in sin(x), cos(x), etc. as expressions in tan(x/2),
• expressions in sinh(x), cosh(x), etc. as expressions in tanh(x/2)

This ticket implements a method for this transformation.

CC: @slel

Component: symbolics

Author: Emmanuel Charpentier, Samuel Lelièvre

Branch/Commit: u/slelievre/32389 @ a60e101

Reviewer: Samuel Lelièvre, Emmanuel Charpentier

Issue created by migration from https://trac.sagemath.org/ticket/32389

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

Branch: u/charpent/half_angle

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

2f7d665

Half_angle : documentation.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Commit: 2f7d665

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:3

This passes ptestlong without any new failure.

==> needs_review, if only to activate patchbots.

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

Author: Emmanuel Charpentier

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:5

pycode and blocks fail : minor mistakes. needs_work

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

0f61904

Half-angle : fix minor lint squabbles.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 2f7d665 to 0f61904

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:7

needs_work to start the patchbots.

[slel]

Description changed:

--- 
+++ 
@@ -1,3 +1,10 @@
-In some circumstances (e. g. integration), it may be useful to replace expressions in sin(h)(x), cos(h)(x), etc... as expressions in tan(h)(x/2).
+In some circumstances (e.g. integration),
+it may be useful to rewrite

-This ticket implements a method for this transformation.
+- expressions in sin(x), cos(x), etc.
+  as expressions in tan(x/2),
+- expressions in sinh(x), cosh(x), etc.
+  as expressions in tanh(x/2)
+
+This ticket implements a method
+for this transformation.

[slel]

Reviewer: Samuel Lelièvre

[slel]

comment:8

This is a good thing to add.

I rebased on Sage 9.4.rc2 and added a commit with:

• changes from \| to | in FriCAS output reverted: they break tests for me
• some refactoring for readability of code ​and examples
  • use half for Integer(1)/Integer(2) (also makes lines shorter)
  • less parentheses, brackets and backslashes in the all(...) test
  • make trig_expand example more compelling by naming a and b
• some reformatting, in particular :: and ​....: ​for example and test blocks
• minor rephrasing, fix spacing and a typo

Set to positive review if you agree with these changes.

[slel]

Changed commit from 0f61904 to a60e101

[slel]

New commits:

aa9339a	Half_angle : code (not yet commented).
a9e702c	Half_angle : documentation.
b5899f7	Half-angle : fix minor lint squabbles.
a60e101	32389: Improve formatting

[slel]

Changed branch from u/charpent/half_angle to u/slelievre/32389

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:10

Replying to @slel:

This is a good thing to add.

Indeed... sympy's and giac integrators use this often.

I rebased on Sage 9.4.rc2 and added a commit with:

• changes from \| to | in FriCAS output reverted: they break tests for me

??? Not for me. Go figure...

• some refactoring for readability of code ​and examples
  • use half for Integer(1)/Integer(2) (also makes lines shorter)

Smart. I should have thought of this, I didn't...

• less parentheses, brackets and backslashes in the all(...) test
• make trig_expand example more compelling by naming a and b
  • some reformatting, in particular :: and ​....: ​for example and test blocks

I'm still struggling with ResStructuredText (too much markup syntaxes : LaTeX, Markdown, Org, Oxygen, WikiFormatting and now this...). Thanks a lot !

• minor rephrasing, fix spacing and a typo

Set to positive review if you agree with these changes.

Thanks ! I do.

BTW : you should be co-author, but I'm almost sure that Trac will balk at the same name in Author and Reviewer fields.

In the same spirit (probably more useful), you may be interested in my attempt to #10038 (demoivre/exponentialize).

[slel]

comment:11

The FriCAS output can be a different ticket. Maybe it depends on the version of FriCAS.

Trac won't mind us being co-authors and co-reviewers of the ticket. It's frequent.

Regarding #10038, I saw you pushed a branch and I'm planning to look at it soon.

[slel]

Changed author from Emmanuel Charpentier to Emmanuel Charpentier, Samuel Lelièvre

[slel]

Changed reviewer from Samuel Lelièvre to Samuel Lelièvre, Emmanuel Charpentier

[slel]

comment:12

The FriCAS output problem might be fixed by #32279 (see also #32379).

[vbraun]

comment:13

Merge conflict