Symbolics

This page gives an overview of open symbolics issues. If you notice a symbolics or calculus issue that is not listed on this page, feel free to add it to the relevant section below.

Other Symbolic pages

Symbolic functions
wiki page to coordinate work on new symbolics functionality.
symbolics/maxima dependencies on maxima
symbolics/nonzero solving the zero comparison problem
Pynac bugs are tracked in the github issue tracker.
symbolics/switch_todo old TODO list for symbolics backend switch to pynac

Wikipedia links and some papers

Links for these tickets

Solve tickets

Unsolved or wrongly solved expressions by type:
- univar. polynomial: #11941, #18900, #10311, #20436
- polynomial in sin(x),cos(x): #3745
- polynomial equation system: #6231, #15499, #9625
- poly fraction system: #15859
- polynomial plus sqrt: #14215
- poly fraction with trig. functions: #14628, #14736, #14738, #16593
- linear system with complicated coefficients: #21873
- exponential equation/system: #18006, #8862, #20068
- mixed system: #16753, #22149
- using conjugate: #18488
- polynomial inequality: #14229
Spurious/missed solutions
- #2617 - solve() can return undefined points as "solutions"
- #11941 - Solve and assumptions too aggressive with cube root of negative numbers
- #18902 - spurious results as inequality solution
- #20755 - Bug in solve due to a bug in symbolic_expression_from_maxima_string
- #21939 - Solving with respect to a dummy variable behaves wrong
- #24939 - solve should not convert floating point to rationals when solving
Enhancements
- #1291 - recurrence solving
- #5201 - matrices as input
- #15859 - allow to_poly_solve force on multiple equations
- #19000 - add an SMT-solver layer
Change defaults/interface
- #5679 - solve should convert additional args to SR
- #6231 - what to do with systems and multiplicities
- #10213 - default solution_dict
- #10750 - additional args are not handled uniformly
- #14736 - trig case where to_poly_solve True works, but not force
- #22018 - Some debug(?) message when solving an inequality
- #23136 - Allow giac algorithm in solve
- #23992 - solve() doesn't solve some system solvable by (standalone) Maxima's solve()
- #24102 - solve(....solution_dict=True) produces nonsense
- #24142 - Improve interface to SymPy solvers
- #24477 - solve(x, [x], solution_dict=True) error

Integration tickets

Bug, solved upstream
- #17469
Bug, not fixed yet upstream (indefinite/symbolic int)
- #15504 - log(1+x)/x
- #15747 - bus or segmentation fault in integral computation
- #17469 - an integral that keeps haunting
- #18822 - sqrt * sqrt
- #21057 - Assumption ignored in indefinite integral computation
- #22138 - Wrong Maxima integral result for even exponents
- #24008 - exp(acos)
- #24117 - integrate(sqrt(1-4*sin(x)^2),x) is wrong
- #24316 - sqrt(sin,cos...)
- #25636 - ECL crash: x^m/sqrt(a + b*x^(2 - m))
- abs_integrate-related errors (see #12731 for possibly disabling or raising warning always with it)
  - #13097 - integral of ln(1+4/5*sin(x))
  - #11590 - sgn() function (not reported upstream?)
  - #14591 - cosh integral incorrect because of abs_integrate
  - #17183 - another abs_integrate error
  - #17468 - log(abs(sin())) problem
  - #17511 - abs(sin(x)) and abs(cos(x)) are flat-out wrong
  - #17910 - unsolved piecewise integrals metaticket
  - #23271 - abs(sin(x)*cos(x))
definite integrals
- #11164 - sin(x)/x
- #11493 - two different results with same numeric integral
- #11655 - Maxima missing rectform simplification after integral()
- #12145
- #13718
- #14213
- #14274 - GSL fail on simpler divergent integrals
- #14764 - Let Mathematica free integration work with definite integrals
- #14976 - integration with non symbolic bounds broken
- #15219 - numerical integral of f(x) = x fails
- #15496 - Incorrect result for divergent integral
- #16788 - segfault in numerical_integral()
- #16905 - really long intervals for integration
- #17606 - Calculation involving nintegral works with Sage 6.3 but not with Sage 6.4
- #18059 - runaway 'unable to simplify to float approximation'
- #18599 - sqrt(cot²)
- #18821 - sqrt(cos)*sin
- #20467 - stackoverflow in sin(kx)/xerf(x²)
- #21440 - cos(2pix)
- #22567 - GSL: Unevaluated integrals to infinity have nonsense numeric value
- #22671 - ((1+x)^(1/5)/(1-x)).integrate(x,2.,3.)
- #22676 - Different results from definite integral methods
- #24008 - exponential integral of arccos
- #24587 - integral(sqrt(1-cos(x)), x, 0, 2*pi)
Changing interface
- #2787 - change to integrate(f,(x,a,b))
- #7763 - unify interface for numerical integration
- #8321 - numerical integration with arbitrary precision
- #21667 - Redundant integrate() & integral() in functional.py and integral.py
- #21905 - Better error message from integrate
floats in integrals: #12152, #14821
Other
- #3732 - Unnecessary interaction
- #13511, #17608 - principal values
- #17109 - Wrong indefinite integral of some odd functions between opposite endpoints
- #17249 - redundant assumption question
- #22410 - Implement Rubi integrator
- #22650 - implement integrals resulting in 2F1 and AppellF1 expressions

simplify/expand tickets

#10038 - wrap Maxima's demoivre and exponentialize into some simplify*
#10073 - held variables aren't restored
#10137 - rewrite function for symbolic expressions
#10268 - add Ginac method to simplify_rational
#10552 - more elementwise simplifications for symbolic matrices
#13099 - Add a loop argument to simplify_full
#14608 - Symbolic functions break the __hash__ contract
#17065 - use Maxima's trigrat() in symbolic simplify
#17066 - simplify hypergeometric() when it's a polynomial
#17737 - wrap Maxima's factorial/gamma conversions/expansions
#18697 - evalf as soon as a FP number and no symbols are present
#19995 - full_simplify involving square root without success
#20520 - apply Maxima's simpsum in sum() and simplify*()
#21307 - Maxima crash: TypeError when simplifying factorial ratio
#21335 - Extend normalize() and use it instead of Maxima in simplify_rational()
#21574 - simplify_log() does not
#22027 - Simplifying 0^x gives 0, with no assumptions on x
#22467, #22495 - simplify_hypergeometric bug
#22607 - Add reduce_trig() to applied "full simplify" methods
#22621 - Improve sqrt products simplification
#22699 - simplify arccos+arcsin when appropriate
#23738 - simplify_full() fails to simplify a log expression
#24231 - Maxima's demoivre() doesn't work with hyperbolic functions

desolve tickets

#8616 - get desolve to automatically deduce variables
#9825 - Maxima temporary variables from diffeq confuse Sage
#11482 - power series solutions
#11653 - ODE whose solution implies integration limits
#14092 - Error with supposedly normal DE problem
#14877 - number of initial conditions in desolve_system
#16653 - immediately get all integral/ODE solutions instead of asking for assumption
#16793 - assumption is not used
#17739 - enhance desolve output from separable ODEs
#20068 - Another diffeq question
#21789 - possible bug in boundary condition handling in Sage (not Maxima)
#22849 - Heaviside in numerical resolutions

limit and summation tickets

#13269 - indeterminate limit result
#14677 - Limit computation causes Sage to crash
#15395 - Wrong limit for sequence
#16422 - cancellation of two indefinite limits
#17428 - wrong limit in derivative
#17553 - substitute_function() can leave limits unevaluated
#17709 - Maxima limit() regression
#17878 - Wrong answer for a simple limit
#17892 - Sage cannot work with Maxima's symbolic limit
#19203 - hold for limit
#20452 - spurious limit computation
#22700 - add sympy limit examples
#26060 - another wrong Maxima limit that is correct in Sympy

series() and taylor()

#6119 - deprecate taylor() in favor of series()
#9555 - Series expansions at singularities don't work
#12589 - series yields wrong result
#15830 - extracting coefficient x-1 out of symbolic series wrong
#15854 - series of x^s, when s is symbolic
#17400 - simplify_full returns odd result from symbolic series input
#18500 - coercion of Laurent series to SR
#19149 - Sister Celine's method for hypergeometric series
#19997 - advanced symbolic series of Order any expression
#19998 - missing operator in symbolic series
#20090 - implement asec/acsc series at infinity
#20846 - Maxima does not handle symbolic series
#21899 - Incorrect Series Expansions of zeta(s) around 1
#22201 - Further series speed improvements

limitations of Piecewise functions

#11225 - improve plotting
#8994 - convolution support
See also the Maxima pw.mac package

conversion to/from other rings

numpy objects: #8824
vector: #16761, vector-valued functions: #11180, #11807, #12302, #11507
#12745 - Coercion problem with Algebraic Real Field
#14277 - Equality of symbolic expressions inside matrix
#14504 - finite field coercion fails for extended fields
#14602 - Symbolic expression to number fields
#17782 - implement expression.polynomial(...,sparse=True)
#17825 - wrong/weird conversion from SR to InfinityRing
#18500 - coercion of Laurent series to SR
#19231 - SR should not coerce into QQbar
#20454 - conversion from SR[] to SR
#20812 - derivative of integer wrt to variable in polynomial ring should belong to that ring, not symbolic ring

fast_float deprecation

#5572 - fast_callable improvements (including deprecating fast_float)
#13559 - fast_float yields infinity when Python does, but should handle bigger numbers
#16899 - Allow complex functions in implicit_plot
#24536 - find_local_maximum/minimum() fails with expressions containing complex numbers

performance

#12786 - solve_mod is horribly slow for linear systems

expression tree and substitutions

#6480 - .subs_expr() method doesn't work for argument of D derivative operator
#9329 - improve documentation of how to access parts of the expression tree
#10169 - Operands and Operator of symbolic expressions
#12577 - make _convert() public
#14270 - Remove function call syntax for symbolic expressions
#15733 - substitution in symbolic function fails with latex_name
#17504 - solve() breaks substitute_function()
#17757 - substitute_function with var argument
#18396 - Handle substitutions of partial sums and products
#21071 - substitution in denominator is skipped
#21754 - Held symbolic powers cannot be approximated numerically
#21758 - Hold symbolic powers unevaluated if evaluation fails
#22102 - Substitutions inside piecewise functions don't work
#22401 - Let substitute_function handle anon functions explicitly
#22926 - Symbolic has_operator()
#23304 - hold=True does not always prevent evaluation
#23964 - f.subs(I==...) does not work
#24255 - Warn with substitution of derived classes using equality
#24283 - Implement Expression.has_function(...)
#24428 - Substitution should be the same as numerical evaluation
#30378 - (x^2).subs({x: sqrt(x)}) returns sqrt(x) instead of x

relation/equality, unknown results, tristate logic

#7660 - arithmetic with equations and inequalities confusing
#12554 - Adding a "swap" method to equation objects
#17700 - wrong symbolic results in case the answer is not known
#11613 - RealInterval expression comparisons broken
#18259 - comparison of symbolic functions
#19040 - defuse bool(x!=0) performance bomb
#19162 - symbolic relations metaticket
#20127 - test_relation: uncaught NoConvergence
#20784 - not all symbolic equations stay unevaluated
#21070 - comparison with wildcard raises error
#21862 - Symbolic methods work inconsistently on relational expressions
#24658 - Don't call Maxima with no-variable symbolic relation tests

variable domains and assumptions

#3277 - context for calculus assumptions
#6862 - Mixing of different domains for symbolic variables
#11941 - Solve and assumptions too aggressive with cube root of negative numbers
#18745 - implement forgetting of assumptions on specific expressions
#18999 - basic assumptions on symbolic functions
#19670 - Consistency and redundancy of verbal assumptions
#20132 - add symbolic domains posint, crational
#21981 - Assuming a variable is prime
#22022 - floor of real x should be known to be at most x
#22025 - minus of real x should be known to be at most abs(x)
#22162 - Return Unknown from ex.is_xyz() if Pynac returns false
#24351 - Even assumption / variable domain / query
#24352 - Implement Expression.is_nonzero(); apply to ex.nonzero()
#24368 - Rational assumption / variable domain / query
#24392 - strange handling of variables in assume
#28538 - Segfault for boolean evaluation of expression with assumptions
#29938 - comparison with infinity does not take assumptions into account

specific Pynac/GiNaC issues

#6756 - Implement diff format symbolic derivative in new symbolics
#10069 - Typesetting with hold=True can be weird
#10268 - add Ginac method to simplify_rational
#11428 - customizable latex for GiNaC functions
#11576 - generate sequences of variables
#12589 - series yields wrong result
#18630 - Expression.is_positive/negative incomplete
#18697 - any FP number in an Expression without symbol should trigger evaluation
#20824 - Expression.coefficient() problems
#21009 - Fix symbolic GCD to accept any expression
#21071 - substitution in denominator is skipped
#21758 - Hold symbolic powers unevaluated if evaluation fails
#22435 - Random build failure in pynac
#23304 - hold=True does not always prevent evaluation
#23368 - More immediate symbolic powers simplification
#23964 - f.subs(I==...) does not work
#24211 - Some trivial identities and simplifications missed by Sage (pynac ?)

Maxima interface

#6862 - Maxima default domain is real, not complex
#9825 - interpret Maxima's temporary variables
#11651 - Decide what to do with e^(y=x)
#12032 - Symbolics code passes ungrammatical expressions to maxima
#12809 - Solve does not give consistent results when a dummy variable is involved
#13071 - maxima interface integration problem
#13773 - Translate maxima's if() function to Sage's cases()
#16335 - dictionary of symbolic expressions (functions) raises Maxima-error
#17892 - Sage cannot work with Maxima's symbolic limit
#19151 - expression manipulations that do not preserve function latex_name and print_latex_func
#19909 - segmentation fault: symbolic sum containing real
#20221 - Wrap ratsubst
#20755 - Bug in solve due to a bug in symbolic_expression_from_maxima_string
#20846 - Maxima does not handle symbolic series
#21444 - SR.wild and maxima don't mix
#21907 - Bug in Maxima interface wrt polylog
#21974 - Assuming x==0, x^x raises a non-informative error from Maxima
#22027 - Simplifying 0^x gives 0, with no assumptions on x
#22763 - Assumptions on symbols not preserved with some unevaluated integrals
#22850 - Change specific heaviside() interface to Maxima
#22857 - Using symbolic variables in domain 'positive' makes Sage crash
#23138 - Cache assumptions and only send to Maxima when needed
#23328 - Undefined limit product $INF * $ZEROB in lim-times

SymPy interface

#16816 - support SymPy's sum of roots
#21412 - Convert piecewise functions to SymPy
#22700 - Add more sympy limit examples
#24078 - Set assumptions in SymPy too when doing assume()
#24142 - Improve interface to SymPy solvers
#24334 - sympy symbol -> SR drops assumptions

Giac interface

#23015 - Convert rootof function from giac
#23016 - Dirac delta derivative conversion from giac
#23136 - Allow giac algorithm in solve

FriCAS interface

#28630 - Wrong conversion from fricas

Other

#11210 - add residues
#17559 - Incorrect caching of variables' latex_name attribute
#17958 - implement declare_var
#18081 - Expression.factor_list() result inconsistent
#18092 - evaluating symbolic expressions within ring of values
#19046 - Fix mma free algorithm when no answer
#19093 - bug in units conversion
#20411 - Injecting shorthands for the most usual units
#20859 - Simplify the logic handling the EvaluationMethods mixin class for Expression
#21067 - Symbolic factor_list() should do integer factorisation of integers/rationals
#22055 - implement Remez algorithm
#22393 - sage_input for SR
#22813 - Pass number of variables to var
#23332 - Calculating eigenvectors of symbolic matrices leads to a crash.
#24537 - Make find_local_maximum/minimum() handle symbolic functions
#24850 - Provide convenient Expression.convert_numeric()

Tickets fixed

#24800 - bug with a system involving square roots, apparently do to an interface issue, Sage not being able to parse conditional answer provided by Maxima
#24425 - Fix inherently failing random_expr doctest
#24440 - Infinite loop from proving an expression
#24773 - Delayed/Conditional Substitution
#5574 - taking symbolic powers should coerce objects to symbolic expressions
#24418 - bug numerical_approx(2^(450232897/4888643760))
#23545 - segmentation fault with coefficients() on symbolic expressions
#23845 - Doctest improvements to symbolic GCD
#24236 - Structural comparison of expressions
#24028 - Held definite integrals don't translate to SymPy
#17935 - recognize SymPy's NonElementaryIntegral
#22322 - allow sympy algorithm in solve
#18787 - Mod numbers are ignored
#22071 - Expression.latex() triggers “dangerous” comparisons
#23224 - wrong symbolic comparison of log
#24147 - Segfault with ex.coefficients
#17565 - ugly LaTeX of unevaluated sums
#8603 - fix Fourier transforms of piecewise
#17935 - recognize Sympy's NonElementaryIntegral
#5091 - find_root should call fast_float
#11332 - 65x penalty in performance for using float instead of RealNumber
#16801 - Not all sympy function results get translated to Sage
#22566 - SymPy's ceiling() is not translated to Sage
#23923 - Interface cases function with SymPy's piecewise
#10035 - Create hold context
#18970 - always simplify log(a^m,a) to m for any a,m coercible to Integer
#21391 - Disallow mixing of pos.char.ring elements and symbolic variables
#20204 - problems with constructing or converting to SymPy expressions
#14305 - Clarify assumptions and domains in Maxima
#23793 - Bug in symbolic GCD computations involving complex I
#23861 - Make Expression normalization work with symbolic powers
#22525 - Improper expressions from SR(string)
#15298 - two copies of I
#19996 - wrong result extracting symbolic coefficient (rational exponent)
#21973 - is_negative() is False when assuming x < 0
#22155 - Add more logic flags to more functions
#23135 - Conjugate does not distribute over a sum
#23496 - sympy patch for abstract function
#22709 - to_poly_solve=True actually raises exception
#17968 - exp(x³) from 1 to 2
#22672 - Definite integral of (1-x)^(1/5)/sqrt(x) crashes with both GSL and Maxima
#22915 - Distribute symbolic sums over the terms of their first (sum) argument
#22733 - Bug with first call to ex.series()
#20179 - add a free_variables() method
#22026 - Even reals are integers
#22894 - Symbolic expression.is_exact()
#22005 - sum(1/((2*n+1)²-4)², n, 0, oo, algorithm='maxima') is wrong
#20084 - residue: mathematically wrong output
#22833 - fix a calculus doctest (giac, laplace, integration)
#22909 - Indexed SR variables
#22706 - Add more conversions from giac
#22995 - Dummy inverse Laplace for giac
#22997 - Parse unevaluated integral from giac
#13733 - integration (but note unwanted interactions)
#22937 - Implement a "distribute" method
#21801 - Maxima summation bug
#22959 - series() yields wrong result depending on precision
#22090 - Gosper algorithm
#22422 - Laplace transform involving time-shifts
#22641 - Fix integration with Mathematica online
#22891 - Add giac interface to integrate
#22057 - Resultant of symbolic polynomials
#22174 - Interface expression conversion to gamma() and normalization
#22017 Unreadable real solution for a very simple equation
#20162 - properties of converted finite field elements are wrong
#10284 - Infinite loop in gcd() via pynac-0.2.1
#20089 - let pynac.pyx use mpmath for arccos
#20455 - rewrite buggy Expression.coefficients() without Maxima
#15605 - (-1)^(2/3) evaluates to 1
#21428 - AssertionError plotting real part of complex function with float coefficients
#14878 - very slow taylor expansion for composite functions
#21730 - Add dedicated symbolic series tests
#21223 - SymmetricFunctions over SymbolicRing broken
#16724 - simplify_rational() takes very long or forever
#20752 - Wrong simplification in symbolic trigonometry involving fractions
#20858 - Option to combine symbolic fractions recursively
#19775 - normalization in Pynac buggy
#20888 - Support GinacFunction.print_latex() customization
#21007 - Unhelpful error when conversion to Symbolic Ring fails
#10034 - simplify_trig of f(a/b*pi) without Maxima
#19464 - ExpressionTreeWalker fails on some functions
#20456 - assume(x>0) sets integer flag
#16491 - unify output of trigonometric functions for complex input
#14801 - Improved piecewise functions
#9424 - numerically evaluate sums (also in functions page)
#16397 - symbolic cmp, stopgap #19465
#16203 - conversion from SR.series() to PowerSeries(SR) gives unexpected result
#15451 - limit wrongly gives ZeroDivisionError
#17402 - SR.power_series cannot handle symbolic series
#18094 - multiplication of powerseries wrapped in SR wrong
#19259 - subrings of the symbolic ring
#17659 - factor out SymbolicSeries from Expression
#12967 - comparison of pi and infinity wrong
#19035 - sync elementary assumptions on symbols/functions with Pynac
#19310 - Pynac hashes are restricted to 32 bits
#17624 - Coerce factorization of polynomial to symbolic expression
#14211 - Crash in GiNaC::Number_T::hash()
#10048 - deprecate substitute_expression()
#12588 - abs(pi*I) should return pi
#18921 - integer variable domain
#18568 - wrong expansion of (x+sqrt(2)*x)^2
#18695 - propagate the variable domain to the assumptions database
#17321 - Pynac RuntimeError: comparing typeid's
#12257 - 1.0*pi should not be pi
#18482 - Unicode art for symbolics
#15304 - is_polynomial() returns wrong results
#14326 - Substituting numeric one in symbolic expression gives symbolic one
#18257 - fix symbolic/pynac.pyx doctests
#17759 - convenience class symbolic ExpressionTreeWalker(Converter)
#17849 - substitute_function should not evaluate expression
#18255 - Remove silly LimitedPrecisionConstant class
#18088 - Inconsistency with 0^0
#13326 - Bug in comparisons of infinite values
#12807 - Taking the real part of a sum of exponentials ...
#17394 - TypeError in Expression.simplify_hypergeometric()
#15355 - representation of CIF-element plus SR-element
#8949, #9769 - numpy object handling
#15047 - LaTeX typeseting of SR.wild should prefix $ with \
#18084 - Fix bad library uses of var()
#18054 - Add is_finite method for the Symbolic Ring
#18040 - Minimal polynomials of matrices over SymbolicRing
#10846 - Conversion of PowerSeries -> SR bug
#17799 - refactor real_set.RealInterval
#9427 - fricas integrator
#3021 - add curl and divergence functions to vectors
#16643 integrate() infinite loop
#15346 - implement simplify_sum and call it from full_simplify
#15571 - Incorrect zero test of complex symbolic expressions
#10629 - performance of checking if (c/d)^(a/b) is rational
#12922 - add implicit derivative
#9824 - improve desolve system documentation for initial conditions
#14630 - add simplify_real
#16201 - default precision for symbolic power series from SR.series()
#16213 - SR.series should simplify its terms
#17399 - fix coefficients for symbolic series
#8969 - != in inputting and outputting with Maxima not handled right
#10444 - make solve documentation better
#13286 - special case of one variable, one equation, variable in list
#10914 - Integral bug
#11233 - Integral bug
#11445 - Integral bug
#11238 - Integral bug
#11656 - additional assumptions needed for simplification
#16941 - Add a hold parameter for symbolic integrals
#9908 - a sum returns hypergeometric functions (also in functions page)
#11894 - about an infinite sum appearing on NMBRTHRY list.
#12708 - waiting for new upstream (Maxima) release.
#13712 - wrong result from infinite sum (Maxima bug).
#13526 simple incorrect limit
#9421 - if c is already a variable it shouldn't come out as a constant
#16007 - give solution constants of ODEs unique names
#11785 - simplifying complex exponentials needs rectform
#12322 - invalid simplification of complex logarithm
#14306 regression in solve
#3520 - simplify_radical does weird things
#11912 - clarify and rename simplify_radical
#21940 - Positive raised by a positive power is not known to be real
#21946 - solve(x==x, x) returns [x == r1]
#1773 - piecewise and symbolic don't play well together
#12123 - another convolution bug
#24726 - Sage silently accepts symbolic expressions with two comparison operators
#23417 - fast construction of symbolic sums
#24768 - Powers of symbolic sums inconsistence
#23313 - Add more conversions from giac II
#23835 - Replace Maxima with Pynac/Singular in Expression.factor()

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Symbolics

Other Symbolic pages

Wikipedia links and some papers

Links for these tickets

Solve tickets

Integration tickets

simplify/expand tickets

desolve tickets

limit and summation tickets

series() and taylor()

limitations of Piecewise functions

conversion to/from other rings

fast_float deprecation

performance

expression tree and substitutions

relation/equality, unknown results, tristate logic

variable domains and assumptions

specific Pynac/GiNaC issues

Maxima interface

SymPy interface

Giac interface

FriCAS interface

Other

Tickets fixed

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