Reimplement elements of Zp and Qp using templates

[roed314]

The goal of this ticket is to reimplement elements of Zp and Qp using the ideas from sage/rings/polynomial/polynomial_template.pxi. This should make p-adics in Sage both easier to maintain and easier to add new classes.

The final patch should not affect the external interface to Zp and Qp.

---

Apply

• attachment: trac_12555.patch
• attachment: trac_12555_review.patch
• attachment: 12555_rebase_6223.patch
• attachment: trac_12555_doc_improvements.patch
• attachment: trac_12555-pdf_fix-ts.patch

Depends on #12625
Depends on #13299
Depends on #14287
Depends on #12575
Depends on #6223

CC: @sagetrac-sydahmad @RalphieBoy @williamstein @sagetrac-JStarx @jpflori

Component: padics

Keywords: sd53 padics templates

Author: David Roe, Julian Rueth

Branch/Commit: public/padics/templates-12555 @ aa65f59

Reviewer: William Stein, Soroosh Yazdani, Julian Rueth, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/12555

[sagetrac-sydahmad]

Replying to @roed314:

The goal of this ticket is to reimplement elements of Zp and Qp using the ideas from sage/rings/polynomial/polynomial_template.pxi. This should make p-adics in Sage both easier to maintain and easier to add new classes.

[roed314]

comment:3

Now includes capped absolute and fixed modulus elements. There are a few problems remaining:

• teichmuller_list is disabled since it had a bug and I didn't want to fix it at the time. I'll track this down later.
• Some coercions aren't working since the element class has changed.

This version should be enough for Justin to compare the performance of the templated and non-templated versions. I'm now going to create another patch on top of this which removes the untemplated versions.

[roed314]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 The goal of this ticket is to reimplement elements of Zp and Qp using the ideas from sage/rings/polynomial/polynomial_template.pxi.  This should make p-adics in Sage both easier to maintain and easier to add new classes.
+
+The final patch should not affect the external interface to Zp and Qp.

[roed314]

Attachment: 12555.patch.gz

Still some bugs, but it should be useable to compare timings

[roed314]

I've fixed all known bugs; currently doctesting

[roed314]

Attachment: 12555_2.patch.gz

Attachment: 12555_printing.patch.gz

[roed314]

Attachment: 12555_remove_base_coerce.patch.gz

[roed314]

Attachment: 12555_conv.patch.gz

Attachment: 12555_remove_base.patch.gz

[roed314]

Attachment: 12555_linkage.patch.gz

[roed314]

Attachment: 12555_template.patch.gz