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symbolics
Sebastian Oehms edited this page Nov 22, 2022
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- 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
- https://en.wikipedia.org/wiki/Symbolic_computation
- https://en.wikipedia.org/wiki/Expression_(mathematics)
- https://en.wikipedia.org/wiki/Richardson%27s_theorem
- https://en.wikipedia.org/wiki/Unification_(computer_science)
- Watt, Making computer algebra more symbolic
- Watt, What happened to languages for symbolic mathematical computation
- [query:?status=needs_review&group=type&component=calculus&component=symbolics&order=priority&col=id&col=summary&col=priority&col=reviewer&col=author&col=dependencies&row=description calculus or symbolics tickets tagged
needs_review] - [query:?status=needs_info&status=needs_work&group=type&component=calculus&component=symbolics&order=priority&col=id&col=summary&col=priority&col=author&col=dependencies&row=description calculus or symbolics tickets tagged
needs_{work,info}] - [query:?status=new&component=calculus&component=symbolics&group=type&col=id&col=summary&col=priority&col=author&col=reviewer&col=dependencies&order=priority calculus or symbolics tickets still tagged
new]
- 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
- 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
- Bug, solved upstream
- 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) = xfails - #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(cot^2^)
- #18821 - sqrt(cos)*sin
- #20467 - stackoverflow in sin(kx)/xerf(x^2^)
- #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
- floats in integrals: #12152, #14821
- Other
- #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:
TypeErrorwhen 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
- #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
- #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
- #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
- #11225 - improve plotting
- #8994 - convolution support
- See also the Maxima pw.mac package
- 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
- #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
- #12786 - solve_mod is horribly slow for linear systems
- #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)})returnssqrt(x)instead ofx
- #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 -
RealIntervalexpression 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
- #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
-
#6756 - Implement
diffformat 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 ?)
- #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
- #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
- #23015 - Convert rootof function from giac
- #23016 - Dirac delta derivative conversion from giac
- #23136 - Allow giac algorithm in solve
- #28630 - Wrong conversion from fricas
- #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
EvaluationMethodsmixin 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()
- #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(x^3^) 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
cis 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_radicaldoes 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()