* fix(combinatorics): Improve precision of stirlingS2
Previously the computation of stirlingS2 used the closed form, which
suffers numerically by dividing a sum of very large terms by a large
factorial, causing roundoff errors for unnecessarily small inputs.
This commit switches to using the recurrence relation for the stirling
numbers of the second kind, and caching the partial results for future
calls. This has the advantage that all intermediate results are smaller
than the final value.
Also adds tests for much larger values of the stirlingS2 function and of
bellNumbers, whose computation depends on stirlingS2.
Resolves#2508.
* fix(stirlingS2): Correct lint errors.
Incorporating unit offsets into the internal "value" of the unit
causes more problems than it solves. This commit ends that practice
and instead only uses the offset when converting units or when
computing the absolute value of a unit.
Further, it makes it an error to compute the sign of a unit with an
offset, since that is inherently ambiguous: there is no way to tell
whether "-5 degC" is a temperature change, in which case it is definitely
negative, or if it is a specific temperature of something, in which case
it is "positive" in the sense of being above absolute zero.
(Unclear how valuable this latter concept is anyway, given that there are
no negative temperatures possible in that sense...)
Adds several tests for the various problems the former practice caused,
including all four basic arithmetic operations on units with offsets.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Also adds tests for math.log() of complex numbers in which the imaginary
part is much larger in absolute value than the real part.
Resolves#2503.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
fix(approx): Make `approx.deepEqual` respect tolerance argument
Tests already contained calls of the form
`approx.deepEqual(A, B, epsilon)` but the comparison tolerance
argument epsilon was being silently ignored. This commit fixes
that oversight and corrects a couple of tests to reflect the finer-
grained testing.
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Also adds the test case that revealed the problem and corrects the other test
case that could have found it except the tolerance had been cranked up very
high.
Resolves#2478.
Resolves#1633
Co-authored-by: Hjortur Jonasson <hjorturjonasson@gmail.com>
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
* doc(map): Clarify the arguments to the callback
Also make the message when there is a type mismatch more detailed.
Resolves#2436.
* test(map): Add tests relevant to new documentation
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
This change fixes a typing problem in complexEigs.js in which
real-valued norms were inadvertently being typed as complex numbers.
Resolves#2439
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* fix(simplify): Collect like factors in sums and cancel like terms in sums
Since polynomials like `x*(2x+x^2)` are usually written out as polynomials
`2x^2+x^3`, adds rules to be more eager to move factors into sums to
collect like factors. To complement this, adds a rule extracting
negative powers from a sum. Together, these accomplish canceling
a common factor in numerator and denominator:
(a*k + b*k^2)/k^4 -> k^-4*(a*k + b*k^2) -> a*k^-3 + b*k^-2 -> k^-3*(a + k*b)
-> (a + k*b)/k^3
Resolves#1423.
* fix(simplify): Adjust for #2394
* chore: Rebase and mark rules with assumptions
This commit should update this PR to be fully compatible with the
current development mainline. Will remove 'WIP'.
* chore(simplify): Additional test cases from PR review
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* docs: Enhance generation to pick up functions with a prefix
For example, prior to this commit, docgenerator.js would miss
simplify.resolve because it is not a direct key of the math
object.
Also incorporates any "throws" attributes in the comments into
the generated documentation, and uses this to document the
new error-case behavior of simplify.resolve to be added in the next
commit.
* fix(resolve): Detect and throw errors for reference loops
Also extends resolve to work inside all node types. Adds tests
for both changes.
* docs: Add embedded docs for simplify.resolve et al.
To support finding the embedded doc from the `math.simplify.resolve`
function itself, required extending the search for objects with
documentation one level deeper in the `help()` function. Added test for
this search.
Also added support for documenting throws in embedded docs.
* refactor(simplify): Move resolve and simplifyCore to top-level
Also reverts changes searching for docs and embedded docs one level
down in the naming hierarchy.
Also splits tests for resolve and simplifyCore into their own files,
reflecting their new top-level status.
* fix(resolve): Remaining changes as requested
Also removed a stray blank line inadvertently introduced in
docgenerator.js
* refactor: Declare resolve and simplifyCore as dependencies of simplify
... rather than explicitly loading them, which is unnecessary now that they
are at top level.
* fix: Add dependencies to factoriesNumber
Also register simplifyCore as a dependency to rationalize
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Note for this to work in a broad variety of contexts, has to also allow
identical expressions to cancel regardless of whether subtraction is
always defined; but this seems safe in general, that x-x is 0 even if x
does not generally have an additive inverse (for example, when working
in the positive context).
Resolves#1260.
Prior to this change, combinations(42,21) did not return an integer,
despite its value being well below MAX_SAFE_INTEGER. Now the
multiplications and divisions are balanced to try to keep the
intermediate results within the safe range.
Adds a couple of tests for larger values of combinations().
Resolves#2413.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* feat(simplify): Allow context option
If the options argument has a key 'context', it value is interpreted
as a context specifying various (non-default) properties of operators.
This context is propagated to all rules and all matching.
Adds some initial tests that the context option affects the behavior
of simplify appropriately. Not all can be activated until in a future
commit we add the ability for the application of a rule to be contingent
on aspects of the context.
Note that the enhanced rule matching necessary to support rules
constrained by non-default operator properties led to a couple of
changes to the output of rationalize() as well. Since the new output
seemed to better match what a person would typical write for the
rationalized form, this commit changed the test rather than attempted
to preserve the exact prior order of terms.
* feat(simplifyCore): strip all parentheses
Prior to this commit, simplifyCore stripped internal parentheses, but
would leave top-level ones. But top-level parentheses don't carry any
semantics, and no tests other than the ones that explicitly checked for
the retention of top-level parentheses were affected by this change.
Not making a special case for the top level also notably streamlined the
code in simplifyCore.
Adds tests for the new parenthesis-stripping behavior, as well as for
other node types that were added earlier but which did not yet have
simplifyCore tests.
* refactor(simplifyCore): Strip any node marked as trivial in context
This replaces special-case tests for unary + and parentheses, and
paves the way for example for 'abs' being marked trivial in a
putative positiveContext
* refactor(simplify): Rename 'context' parameter to rules and document it.
The new name is 'imposeContext' -- the motivation for the change is to
distinguish the parameter for 'assuming', which will be added as a new
parameter to control rule application based on context.
* feat(simplify): Allow context-based conditions on rule application.
Adds a new property of rules specified as objects: `assuming`. Its
value should be a context, and every property specified in that context
must match the incoming context, or else the rule will not be applied.
Updates the constant floating rules to require their operators be commutative,
as a test of the feature, and adds a unit test for this.
* feat(simplify): annotate rules with underlying assumptions
Also activates a number of tests of simplifications that should
or should not occur in various contexts.
To get all tests to pass, I could no longer find a rule ordering
that worked in all cases, without the ability to mark an individual
rule as applying repeatedly until just that rule stabilized. So this
commit also adds that ability, and uses it to eliminate the tricky rule
of expanding n1 + (n2 + n3)*(-1) to n1 + n2*(-1) + n3*(-1) late in the
rule ordering, in favor of the more intuitive (complete) expansion of
(n1 + n2)*(-1) to n1*(-1) + n2*(-1) early in the rule ordering, before
constant folding and gathering of like terms.
* feat(simplify): Add contexts for specific domains
In particular, adds a `simplify.realContext` and a `simplify.positiveContext`
which (attempt to) guarantee that no simplifications that change the value
of the expression, on any real number or any positive real number,
respectively, will occur.
Adds multiple tests for these contexts, including verification that the
simplification in either context does not change some example values of
any of the expressions in any simplify test.
This testing uncovered that it is unaryPlus that must be marked as trivial
for simplifyCore to work properly, so that marking is added as well.
* chore: Alter value consistency tests for browsers/older Node
The problem was NaN != NaN in some JavaScripts but not others,
so test for "both values NaN" explicitly before using deepEqual.
* fix: Implement requested changes from review
Added documentation about scope and context in top-level algebra functions
page; made variable name less abbreviated; performed suggested refactoring.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
This function returns the number of leaves in the parse tree of an
expression. The motivation is to provide an initial complexity measure
that could be used to decide whether or not to apply some simplification
rules. Docs, embedded docs, and test cases are provided.
Resolves#2389.
* fix(simplify): Correct regression in simplify
Also adds a 'debugConsole' option to simplify() so that it is possible
to see the effect of each rule. This was critical to identifying the problem,
which was that recent changes ended up with `simplifyConstant` in the
wrong position in the list of rules. Correcting that also removed the need
for the two rules coalescing negations with constants.
Resolves#2393.
* fix(simplify): Correct another regression based on rule ordering
Disccovered that `x - (y-y+x)` had also stopped simplifying due
to recent changes, again because of re-ordering of the rules. So
added it to the tests, and fixed the rule ordering (adding a more
extensive comment about it). A big part of the reason that rule
ordering is so sensitive is that the reduction engine only checks
once in each pass for each rule whether it matches. So an alternate
fix to changing the rule ordering back would have been to re-check
each rule after it's applied (in case its application created new
instances of the rule) but since the re-ordering worked, that seemed
simpler as a fix for now.
* fix(simplify): Allow simplify to work in arrays, objects, and indexing
Mostly ArrayNode, ObjectNode, AccessorNode, and IndexNode nodes are
simply transparent to simplification -- they simply allow it to occur
within subexpressions. Then main exception is that if an array or object
is indexed by a constant, the expression can be replaced by the
corresponding subitem, e.g. `[3,4,5][2]` simplifies to `4`.
This at least partially resolves#1913 (see my latest comment there).
* fix(simplify): Resolve operations on constant arrays
This involves allowing ArrayNodes containing only constant entries
to temporarily convert to Matrix type inside of simplifyConstant, so that
function and operator calls can occur on them.
I also had to add a special case for the function `size` because
it can be computed even on symbolic arrays, since the result depends
only on the shape, not the entries.
Deals with additional cases of #1913; unclear if there are remaining
aspects of that issue on which further work is desirable.
* chore: fix alphabetization of dependencies
And restores inadvertent deletion of a blank line.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
The key is that the rule-matching engine is optimized for finding matches
on the lefts of terms, but the central term-collection rule
`n1*n3 + n2*n3 -> (n1+n2)*n3` was written with the key common term rightmost.
Reversing this rule to `n3*n1 + n3*n2 -> n3*(n1+n2)` therefore does most
of the work of improving like-term collection. It also better corresponds
to typical mathematical presentation: common terms tend to be pulled out
to the left in common practice.
Floating constants to the right of a product initially (before they are
moved back to the left for human-preferred output) and ensuring that
negations are subsumed into constants whenever possible did the rest.
Also, rule context was not being propagated into the simplification
engine; this commit corrects that.
Resolves#1179.
Resolves#1290.
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* fix(simplify): Leave string constants as strings.
Note that because the `size` built-in function called on a string returns
a Matrix, which is represented in math.js expressions as an Array, this
commit has to add ArrayNode as a dependency of `simplify` (and hence
also of `rationalize`).
In addition, it requires changing the handling of ArrayNodes
and AccessorNodes in `simplifyConstant` from "unimplemented" to just a
pass-through (since a full implementation of simplification in Arrays and
indexing seemed beyond the scope of this change, but `simplify` must not
throw an error on `size("foo")`). Hence, this commit also adds skipped unit
tests for some expressions with arrays and indexing that should ultimately
simplify.
It also removes the skip on the test group "should not change the value of
numbers when converting to fractions (3)" since all of those tests already
appear to pass.
Resolves#2152.
Changes the behavior in #1913 from throwing an error to allowing Arrays and
indexes but not simplifying inside them.
* chore: Fix lint and remove explanatory comment
* refactor(gamma function): use lanczos approximation with comments
* tests: additional checks for specific numbers
* tests: check for value close to re(0.5)
* refactored intersect, fixed it not returning null for matrix input
* intersect: improved flattening algorithm, added tests
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* fix toTex(): remove row delimiter on the last row
* remove row delimiter on the last row (use map and join instead of forEach)
* fix ArrayNode.toTex() unit tests incorrectly expecting a row delimiter on the last row
* added toTex() tests for nested cases
* fixed ArrayNode.toTex() for nested cases
* removed redunant variable
* changed BigNumber to a class that extends Decimal.clone(...)
* it works... if you patch decimal.js
* added a test that checks if sum of Decimals works
* minor improvement of code quality
* updated Decimal.js to 10.3
* removed the optional chaining operator to keep compat w/ Node 12
* removed try/catch from isBigNumber
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* Add support for scopes with get and set methods
* Fix build for node v12
* Fixup cli and parser tests
* Add tests for simplify and evaluate
* Add example for a custom scope object
* Function calls need child scopes
* Transitionary step: Separate Safe and Scope Property calls
* Renamed identifiers in FunctionNode
* Evaluate with ObjectScopeWrapper
* Simplify tests passing
* Assume all scopes are map-like. Except parser
* Remove isMapLike check in customs.*SafeProperty() methods
* Change MapLike to Map
* Move keywords from an Object to a Set
* Move ScopeProperty functions in to scope.js
* Removed deprecation warning
* Rename scope.js to map.js
* Rename ScopeProperty to MapProperty
* Add tests and docs for map.js
* Put back the micro-optimization of function calls
* Use Map in the parser
* Called scope methods directly in cli.js
* Coercing of scope into a Map is done in Node, not evaluate
* Move createSubScope to its own file
* Fixup following self-review
* Add scope docs
* Final self-review changes
* Address reviewer comments
* Remove MapProperty witness marks
* Converted broken benchmark possibly lost in a rebase
* Use bare map as scope in benchmark
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* made dense and sparse matrices iterable, fixed#1184
* added matrixFromFunction, fixes#2153
* added tests for matrixFromFunction
* added matrixFromRows
* added matrixFromColumns
* added rows() and columns() for dense matrix
* improved sparse documentation a tiny bit
* fix linting issues
* added matrixFromRow/Column to seealso of row and column
* removed unnecessary duplication from matrixFromRows/Columns
* added babel runtime
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* split the eigs function into multiple algorithms
* moved checks and coersions to eigs.js, made them more robust
* fix little bugs, make im and re more robust
* Implemented matrix balancing algorithm
* fix typos
* a draft of reduction to Hessenberg matrix
* finished implementation of reduction to Hessenberg
* fix Hessenberg elimination for complex numbers
* implemented non-shifted explicit QR algorithm for real matrices
* implemented vector computation, won't work untill usolve is fixed
* refactored to match yarn lint
* some minor changes
* solve merge conflicts
* refactored and re-fixed #1789
* some old uncommited changes
* fix small problems introduced by merging
* done some polishing
* improved jsdoc description of eigs
* little changes in jsdoc
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* Miller–Rabin primality test
* add tests for some big numbers
* Update isPrime.js
* Update isPrime.js
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* added support for word size suffix in getToken
* start modifying number(string) to support word size suffix for signed integers
* word size suffixes for Number
* initial support for BigNumber
* fix linter issues
* remove unused variable
* start extending bitwise operators for Number for values greater than 32 bits
* Revert "start extending bitwise operators for Number for values greater than 32 bits"
This reverts commit 6fac1a7b10665a221ab5de521c08fa9fcf959eb1.
* add a test for 53 bit literal
* added an optional second argument to bin, oct, and hex to allow formatting signed numbers with custom word size
* removed size checks
* Attempted to extend bin, oct, hex format functions to work with BigNumber, but not working fully.
Apparently Decimal.js toString method doesn't take a base parameter like js number does. I guess I have to do the formatting myself.
* Added n2base function to do formatting for BigNumber.
* Added check for zero in n2base.
* Removed old failing tests.
* Added some tests (failing).
* Extended 'format' function with 'base' and 'wordSize' options and changed 'bin', 'oct', and 'hex' to use 'format' function.
* Fixed lint issues.
* Fixed issues related to the merge.
* Corrected a test.
* Fixed bignumber formatter.
* Added tests for math.format with 'base' and 'wordSize' options.
* Fixed lint issue.
* Changed 'base' option to 'bin', 'oct', and 'hex' values for 'notation' option of 'format' function.
* Added word size suffix to the output of format, bin, oct, and hex.
* Updated documentation.
