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# Edit detail for #102 solve(sinh(z)=cosh(z), z) revision 6 of 9

 1 2 3 4 5 6 7 8 9 Editor: japp Time: 2008/10/16 11:16:06 GMT-7 Note:

```added:

From japp Thu Oct 16 11:16:06 -0700 2008
From: japp
Date: Thu, 16 Oct 2008 11:16:06 -0700
Subject:
Message-ID: <20081016111606-0700@axiom-wiki.newsynthesis.org>

Status: fix proposed => fixed somewhere

```

 Submitted by : (unknown) at: 2007-11-17T21:51:30-08:00 (15 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : general Severity : critical serious normal minor wishlist Status : open pending closed Optional subject :   Optional comment :

>> Error detected within library code: No identity element for reduce of empty list using operation append

This one and bug #137 can be resolved by using the three-argument form of reduce in SOLVETRA, for example:
```     solveList(lexpr:L RE, lvar:L S):L L EQ RE ==
ans1 := solveRetract(lexpr, lvar)
not(ans1 case "failed") => ans1 :: L L EQ RE
lfrac:L Fraction Polynomial RE :=
[makeFracPoly(expr, lvar) for expr in lexpr]
trianglist := triangularSystems(lfrac, lvar)
-- "append"/[solve1Sys(plist, lvar) for plist in trianglist]
l: L L L EQ RE := [solve1Sys(plist, lvar) for plist in trianglist]
reduce(append, l, [])
```

and similarly in all places, where `"append"/` is used. Maybe there is an alternative fix, `"append"/` does not call reduce, does it?

property change --kratt6, Fri, 17 Jun 2005 08:14:03 -0500 reply
Status: open => fix proposed

Why is "append" written with quotation marks? --Bill Page, Mon, 17 Oct 2005 13:34:27 -0500 reply
Martin, can you explain to me what this function call in the original code is supposed to do:
```  "append"/[solve1Sys(plist, lvar) for plist in trianglist]
```

What it does is easily explained: `"foo"/l` maps the function `foo` over the list `l`. However, it appears that it doesn't use reduce but rather some lisp primitive. It is hard to trace, since it doesn't work in the interpreter. I suppose that it is some leftover of the elder days of `spad`. In any case, when you `grep` the `algebra` directory, there doesn't appear to be a three argument form of this construct, so I propose to (gradually) replace it by `reduce` everywhere.

Martin

"foo"/list is a BOOT construction --Bill Page, Tue, 18 Oct 2005 17:50:00 -0500 reply
This construct occurs frequently in the BOOT code in src/interp so I guess that this is actually a carry-over from the BOOT language.

In http://wiki.axiom-developer.org/axiom--test--1/src/algebra/Aggcat2Spad `reduce` is defined as either:

```      reduce(fn, v, ident) ==
val := ident
for i in minIndex v .. maxIndex v repeat
val := fn(qelt(v, i), val)
val
```

for array-like structures or recursively (for lists):

```      reduce(fn, l, ident) ==
empty? l => ident
reduce(fn, rest l, fn(first l, ident))
```

It seems doubtful to me that either of these would be optimized by SPAD to a simple lisp primitive (but I could be wrong). Anyway I agree that it makes more sense to use `reduce` in the algebra code especially since there is no "/" operation defined in the domain `List`, although this might introduce more circularity (mutual recursion) in the algebra code.

I wonder if it would work to define the operation:

```  "/":((S, R) -> R, A, R) -> R
```

as a synonym for `reduce` in `List` and then recompile most of the algebra code or would SPAD die of embarrassment?

It should work, given that the compiler does not stumble over some bug. However, I don't think it is the right direction to take anyway:

• The bugs mentioned here won't go away, since you would have to provide the third argument, and
• I think that `reduce` is easier to understand for the casual reader.

Concerning the optimization: in an ideal world, reduce would be optimized away. We are not in an ideal world, and we will never be, but we should strive to make it better...

fixed in patch 46 --kratt6, Fri, 27 Oct 2006 06:46:08 -0500 reply
Status: fix proposed => closed

Status: closed => open

This patch was made to Axiom on 10/30/2005. In the current version of Axiom the patch exists. However, the error still occurs.

Fixed in revision 51 of FriCAS? --greg, Thu, 20 Dec 2007 08:27:44 -0800 reply