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Commitde5d6e5

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fix/refactor: disregard symbols less-so for 'canonicalPower'
jointly, do more checks on operand types (particularly for functionexprs.), more strictly check for type 'number'; less eager insimplifying FN-expressions as operands.
1 parenta25459b commitde5d6e5

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2 files changed

+129
-37
lines changed

2 files changed

+129
-37
lines changed

‎src/compute-engine/boxed-expression/arithmetic-power.ts‎

Lines changed: 17 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -68,17 +68,13 @@ export function canonicalPower(
6868
// here)
6969
if(
7070
b.isFunctionExpression||
71-
!b.isConstant||//(!notably, should exclude symbol assumptions)
71+
b.symbol!==null||
7272
!b.type.matches('number'asType)
7373
)
7474
returnunchanged();
7575

76-
// 'a' is constant and of type 'number'. Used often.
77-
// (note that this could still be a numeric expression, too...)
78-
constaIsNum=a.isConstant&&a.type.matches('number'asNumericType);
79-
8076
// Zero as base
81-
if(aIsNum&&a.is(0)){
77+
if(a.isNumberLiteral&&a.is(0)){
8278
if(b.type.matches('imaginary'asNumericType)||b.isNaN)returnce.NaN;
8379

8480
if(b.is(0))returnce.NaN;
@@ -97,9 +93,19 @@ export function canonicalPower(
9793
returnunchanged();// No other canonicalization cases with this base
9894
}
9995

96+
// 'a'/base has an associated number value (excludes numeric functions)
97+
// (this should at this stage include library-defined symbols such as 'Pi')
98+
//@note: include 'Negate', because this could be wrapped around a number-valued symbol, such as
99+
//'Pi'...
100+
//^there could exist other exceptions: perhaps consider a util. such as 'maybeNumber'?
101+
constaIsNum=
102+
a.type.matches('number'asNumericType)&&
103+
(a.isFunctionExpression===false||a.operator==='Negate');
104+
100105
// Zero as exponent
101106
if(b.is(0)){
102-
if(aIsNum)returna.isFinite ?ce.One :ce.NaN;
107+
// If 'isFinite' is a boolean, then 'a' has a value.
108+
if(aIsNum&&a.isFinite!==undefined)returna.isFinite ?ce.One :ce.NaN;
103109
returnunchanged();
104110
}
105111

@@ -109,7 +115,8 @@ export function canonicalPower(
109115
if(aIsNum&&a.is(1))returnb.isFinite ?ce.One :ce.NaN;
110116

111117
// One as exponent
112-
if(b.is(1))returna;
118+
// (Permit the base to be a FN-expr. here, too...)
119+
if(b.is(1)&&a.type.matches('number'asNumericType))returna;
113120

114121
// -1 exponent
115122
if(b.is(-1)){
@@ -176,8 +183,8 @@ export function canonicalPower(
176183
returnce.NaN;
177184
}
178185

179-
//'Infinity^Complex'
180-
if(a.isInfinity){
186+
//'AnyInfinity^{~oo}' (i.e. ComplexInfinity)
187+
if(a.isNumberLiteral&&a.isInfinity){
181188
// If the exponent is pure imaginary, the result is NaN
182189
//(↓fix?:ensure both these cases narrow down to 'b' being a num./symbol literal)
183190
if(b.type.matches('imaginary'asNumericType))returnce.NaN;

‎test/compute-engine/canonical-form.test.ts‎

Lines changed: 112 additions & 27 deletions
Original file line numberDiff line numberDiff line change
@@ -240,12 +240,38 @@ describe('CANONICAL FORMS', () => {
240240

241241
describe('Power',()=>{
242242
constengine=newComputeEngine();
243-
engine.declare('x',{constant:true,value:0});
244-
engine.declare('y',{constant:true,value:1});
245243

246-
engine.declare('p',{constant:true,value:Infinity});
247-
engine.declare('n',{constant:true,value:-Infinity});
248-
engine.declare('c',{constant:true,value:-Infinity});
244+
/*
245+
* 'Power'-scoped symbol declarations
246+
*/
247+
//@note: declarations are necessarily marked with 'holdUntil: never' - for these test cases - in
248+
//order to permit substitution during (before) application of canonical-forms.
249+
//^Necessary because 'a^x' is not a valid simplification (cannot assume that 'x' is bound), but
250+
//if x is substituted, then that's fine...
251+
engine.declare('x',{constant:true,value:0,holdUntil:'never'});
252+
engine.declare('y',{constant:true,value:1,holdUntil:'never'});
253+
254+
engine.declare('p',{
255+
constant:true,
256+
value:Infinity,
257+
holdUntil:'never',
258+
});
259+
engine.declare('n',{
260+
constant:true,
261+
value:-Infinity,
262+
holdUntil:'never',
263+
});
264+
engine.declare('c',{
265+
constant:true,
266+
value:-Infinity,
267+
holdUntil:'never',
268+
});
269+
270+
//Control-case symbols (holdUntil value of default 'evaluate', and henceforth 'value' not to be
271+
//consulted at this stage)
272+
engine.declare('j',{constant:true,value:0});
273+
engine.declare('k',{constant:true,value:1});
274+
249275
constcheckPower=(
250276
input:string,
251277
priorForms:CanonicalForm[]=['Number']
@@ -267,12 +293,21 @@ describe('CANONICAL FORMS', () => {
267293
canonForms = ComplexInfinity
268294
canonical = ComplexInfinity
269295
`);
270-
// x === 0
296+
// x === 0 (simplifies because is substituted beforehand ('holdUntil = never'))
271297
expect(checkPower('x^3')).toMatchInlineSnapshot(`
272298
box = ["Power", "x", 3]
273299
canonForms = 0
274300
canonical = 0
275301
`);
302+
303+
// Control
304+
//
305+
//'j=0', but should _not_ substitute (i.e. beforehand) & therefore no op. should take place
306+
//(its 'holdUntil' property is set to the default 'evaluate')
307+
expect(checkPower('j^3')).toMatchInlineSnapshot(`
308+
box = ["Power", "j", 3]
309+
canonForms = ["Power", "j", 3]
310+
`);
276311
});
277312

278313
test('x^0',()=>{
@@ -286,11 +321,18 @@ describe('CANONICAL FORMS', () => {
286321
canonForms = NaN
287322
canonical = NaN
288323
`);
324+
//↓Only simplifies because 'x' substitutes with its value during partial-canonicalization;
325+
//prior to app. of CanonicalForms.
289326
expect(checkPower('16^x')).toMatchInlineSnapshot(`
290327
box = ["Power", 16, "x"]
291328
canonForms = 1
292329
canonical = 1
293330
`);
331+
//!@note: this should be ok to apply, despite 'Pi' being a constant which does *not* have a
332+
//!'holdUntil' value set to 'never', because... this is a library/engine-level defined
333+
//!constant in which its type/value is always known: even in non-canonical expressions.
334+
//I.e., if this were a user-defined constant, this would not be OK, since its value would have
335+
//to be referenced.
294336
expect(checkPower('\\pi^0')).toMatchInlineSnapshot(`
295337
box = ["Power", "Pi", 0]
296338
canonForms = 1
@@ -301,6 +343,15 @@ describe('CANONICAL FORMS', () => {
301343
canonForms = 1
302344
canonical = 1
303345
`);
346+
347+
/*
348+
* Control-case
349+
*/
350+
//j===0, but is *held*
351+
expect(checkPower('2^j')).toMatchInlineSnapshot(`
352+
box = ["Power", 2, "j"]
353+
canonForms = ["Power", 2, "j"]
354+
`);
304355
});
305356

306357
test('1^x',()=>{
@@ -342,15 +393,41 @@ describe('CANONICAL FORMS', () => {
342393
canonForms = PositiveInfinity
343394
canonical = PositiveInfinity
344395
`);
345-
expect(checkPower('{-a/4}^1')).toMatchInlineSnapshot(`
346-
box = ["Power", ["Divide", ["Negate", "a"], 4], 1]
347-
canonForms = ["Divide", ["Negate", "a"], 4]
348-
canonical = ["Multiply", ["Rational", -1, 4], "a"]
349-
`);
350-
expect(checkPower('{-\\pi}^1')).toMatchInlineSnapshot(`
351-
box = ["Power", ["Negate", "Pi"], 1]
352-
canonForms = ["Negate", "Pi"]
353-
canonical = ["Negate", "Pi"]
396+
397+
//@note: This correctly simplifies, unlike would be expected of 'x^1' (where x is a
398+
//user-declared numeric constant with a default 'holdUntil' value of 'evaluate'), because 'Pi'
399+
//is a library-defined constant, consequently always being canonical & bound (and ∴ having a
400+
//type/value), even in *non-canonical* exprs.
401+
//^!Note that currently, 'x^1' *will simplify* at present, but this would not be considered
402+
//correct behaviour (compute-engine/pull/238#discussion_r2034335185). This is because
403+
//canonicalization of symbols (including partial-canonicalization) is presently, erroneously,
404+
//synonymous with 'binding': permitting its type/value to be determined at this stage.
405+
expect(checkPower('{\\pi}^1')).toMatchInlineSnapshot(`
406+
box = ["Power", "Pi", 1]
407+
canonForms = Pi
408+
canonical = Pi
409+
`);
410+
411+
//↓🙁: cannot be simplified, at least via the route of checking the 'type' of the base/'-\pi',
412+
//because is a non-canonical function-expr. (non-bound to 'Power' definition)
413+
414+
// expect(checkPower('{-\\pi}^1')).toMatchInlineSnapshot(`
415+
// box = ["Power", "Pi", 1]
416+
// canonForms = Pi
417+
// canonical = Pi
418+
// `);
419+
420+
/*
421+
* Control
422+
*/
423+
//!@note:
424+
//Not currently simplified, despite 'j' being an 'integer'-typed constant, because the base is
425+
//a non-canonical function and therefore unbound to a definition; consequently with its 'type'
426+
//non-determinable.
427+
expect(checkPower('{-j/4}^1')).toMatchInlineSnapshot(`
428+
box = ["Power", ["Divide", ["Negate", "j"], 4], 1]
429+
canonForms = ["Power", ["Divide", ["Negate", "j"], 4], 1]
430+
canonical = ["Multiply", ["Rational", -1, 4], "j"]
354431
`);
355432
});
356433

@@ -377,10 +454,10 @@ describe('CANONICAL FORMS', () => {
377454
canonForms = ["Rational", 1, 3]
378455
canonical = ["Rational", 1, 3]
379456
`);
380-
expect(checkPower('{x * 4}^{-1}')).toMatchInlineSnapshot(`
381-
box = ["Power", ["Multiply", "x", 4], -1]
382-
canonForms = ["Divide", 1, ["Multiply", 4, "x"]]
383-
canonical = ["Divide", 1, ["Multiply", 4, "x"]]
457+
expect(checkPower('{j * 4}^{-1}')).toMatchInlineSnapshot(`
458+
box = ["Power", ["Multiply", "j", 4], -1]
459+
canonForms = ["Divide", 1, ["Multiply", 4, "j"]]
460+
canonical = ["Divide", 1, ["Multiply", 4, "j"]]
384461
`);
385462
});
386463

@@ -426,7 +503,10 @@ describe('CANONICAL FORMS', () => {
426503
canonical = ComplexInfinity
427504
`);
428505

429-
//Constant-symbol value cases.: p=PositiveInfinity
506+
/*
507+
* Constant-symbol value cases.
508+
*/
509+
// p === +Infinity (& 'holdUntil: never')
430510
expect(checkPower('1^{p}')).toMatchInlineSnapshot(`
431511
box = ["Power", 1, "p"]
432512
canonForms = NaN
@@ -470,13 +550,17 @@ describe('CANONICAL FORMS', () => {
470550
canonForms = 0
471551
canonical = 0
472552
`);
473-
expect(checkPower('{-\\pi}^{-\\infty}')).toMatchInlineSnapshot(`
474-
box = ["Power", ["Negate", "Pi"], "NegativeInfinity"]
475-
canonForms = ["Power", ["Negate", "Pi"], "NegativeInfinity"]
476-
canonical = 0
477-
`);
478-
479-
//Constant-symbol value cases.: n=NegativeInfinity, x=0
553+
//🙁: cannot be simplified, base/'Negate' is non-canonical and 'type' cannot be determined.
554+
// expect(checkPower('{-\\pi}^{-\\infty}')).toMatchInlineSnapshot(`
555+
// box = ["Power", ["Negate", "Pi"], "NegativeInfinity"]
556+
// canonForms = ["Power", ["Negate", "Pi"], "NegativeInfinity"]
557+
// canonical = 0
558+
// `);
559+
560+
/*
561+
* Constant-valued symbol operands
562+
*/
563+
//x=0, n=NegativeInfinity ('holdUntil: never'),
480564
expect(checkPower('x^{n}')).toMatchInlineSnapshot(`
481565
box = ["Power", "x", "n"]
482566
canonForms = ComplexInfinity
@@ -541,6 +625,7 @@ describe('CANONICAL FORMS', () => {
541625
`);
542626

543627
//Include 'Add' in order that complex-numbers may be identified for these cases.
628+
//(^note that this may later be included as part of the 'Number' form)
544629
check=(input:string)=>
545630
checkPower(input,['InvisibleOperator','Number','Add']);
546631

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