class JAS::Ring
Represents a JAS polynomial ring: GenPolynomialRing.
Methods to create ideals and ideals with parametric coefficients.
Attributes
auto_inject[RW]
inject variables into environment
auto_lowervar[RW]
avoid capital letter variables
engine[R]
the Java factoy object, gcd engine, sqf engine, factorization engine
factor[R]
the Java factoy object, gcd engine, sqf engine, factorization engine
ring[R]
the Java factoy object, gcd engine, sqf engine, factorization engine
sqf[R]
the Java factoy object, gcd engine, sqf engine, factorization engine
Public Class Methods
getEngineFactor(r)
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Get the polynomial factorization engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1725 def Ring.getEngineFactor(r) 1726 if r.is_a? RingElem 1727 r = r.elem; 1728 end 1729 if not r.is_a? GenPolynomialRing 1730 return nil; 1731 end 1732 begin 1733 i = FactorFactory.getImplementation(r.coFac); 1734 rescue => e 1735 i = nil 1736 end 1737 #puts "factor engine: #{i}"; 1738 return i; 1739 end
getEngineGcd(r)
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Get the polynomial gcd engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1682 def Ring.getEngineGcd(r) 1683 if r.is_a? RingElem 1684 r = r.elem; 1685 end 1686 if not r.is_a? GenPolynomialRing 1687 return nil; 1688 end 1689 begin 1690 i = GCDFactory.getProxy(r.coFac); 1691 #i = GCDFactory.getImplementation(r.coFac); 1692 rescue => e 1693 i = nil 1694 end 1695 #puts "gcd engine: #{i}"; 1696 return i; 1697 end
getEngineSqf(r)
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Get the polynomial squarefree engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1704 def Ring.getEngineSqf(r) 1705 if r.is_a? RingElem 1706 r = r.elem; 1707 end 1708 if not r.is_a? GenPolynomialRing 1709 return nil; 1710 end 1711 begin 1712 i = SquarefreeFactory.getImplementation(r.coFac); 1713 rescue => e 1714 i = nil 1715 end 1716 #puts "sqf engine: #{i}"; 1717 return i; 1718 end
new(ringstr="",ring=nil)
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Ring constructor.
ringstr string representation to be parsed. ring JAS ring object.
# File examples/jas.rb 1649 def initialize(ringstr="",ring=nil) 1650 if ring == nil 1651 sr = StringReader.new( ringstr ); 1652 tok = RingFactoryTokenizer.new(sr); 1653 pfac = tok.nextPolynomialRing(); 1654 #tok = GenPolynomialTokenizer.new(sr); 1655 #@pset = tok.nextPolynomialSet(); 1656 @ring = pfac; 1657 else 1658 if ring.is_a? Ring 1659 @ring = ring.ring 1660 else 1661 @ring = ring; 1662 end 1663 end 1664 # parameter ",fast=false" not possible w/o keyword params 1665 #if fast == true 1666 # return 1667 #end 1668 @engine = Ring.getEngineGcd(@ring); 1669 @sqf = Ring.getEngineSqf(@ring); 1670 @factor = Ring.getEngineFactor(@ring); 1671 variable_generators() 1672 if self.class.auto_inject or self.class.superclass.auto_inject # sic! 1673 inject_variables(); 1674 end 1675 end
Public Instance Methods
==(other)
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Test if two rings are equal.
# File examples/jas.rb 1791 def ==(other) 1792 if not other.is_a? Ring 1793 return false; 1794 end 1795 return @ring.equals(other.ring); 1796 end
CRT(polystr="", list=nil, rem=nil)
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Chinese remainder theorem.
# File examples/jas.rb 2091 def CRT(polystr="", list=nil, rem=nil) 2092 if list == nil 2093 sr = StringReader.new( polystr ); 2094 tok = GenPolynomialTokenizer.new(@ring,sr); 2095 @list = tok.nextPolynomialList(); 2096 else 2097 @list = rbarray2arraylist(list,nil,rec=2); 2098 end 2099 if rem == nil 2100 raise ArgumentError, "No remainders given." 2101 else 2102 @remlist = rbarray2arraylist(rem,nil,rec=1); 2103 end 2104 #puts "list = " + str(@list); 2105 #puts "remlist = " + str(@remlist); 2106 #puts 2107 h = PolyGBUtil.chineseRemainderTheorem(@list, @remlist); 2108 if h != nil 2109 h = RingElem.new(h); 2110 end 2111 return h; 2112 end
CRTinterpol(polystr="", list=nil, rem=nil)
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Chinese remainder theorem, interpolation.
# File examples/jas.rb 2117 def CRTinterpol(polystr="", list=nil, rem=nil) 2118 if list == nil 2119 sr = StringReader.new( polystr ); 2120 tok = GenPolynomialTokenizer.new(@ring,sr); 2121 @list = tok.nextPolynomialList(); 2122 else 2123 @list = rbarray2arraylist(list,nil,rec=2); 2124 end 2125 if rem == nil 2126 raise ArgumentError, "No remeinders given." 2127 else 2128 @remlist = rbarray2arraylist(rem,nil,rec=1); 2129 end 2130 #puts "ring = " + str(@ring.toScript()); 2131 #puts "list = " + str(@list); 2132 #puts "remlist = " + str(@remlist); 2133 #puts 2134 h = PolyGBUtil.CRTInterpolation(@ring, @list, @remlist); 2135 if h != nil 2136 h = RingElem.new(h); 2137 end 2138 return h; 2139 end
algebraicRoots(a,eps=nil)
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Compute algebraic real and complex roots of univariate polynomial.
# File examples/jas.rb 2001 def algebraicRoots(a,eps=nil) 2002 if not a.is_a? RingElem 2003 a = RingElem.new(a); 2004 end 2005 return a.algebraicRoots(eps); 2006 end
complexRoots(a,eps=nil)
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Compute complex roots of univariate polynomial.
# File examples/jas.rb 1991 def complexRoots(a,eps=nil) 1992 if not a.is_a? RingElem 1993 a = RingElem.new(a); 1994 end 1995 return a.complexRoots(eps); 1996 end
decimalRoots(a,eps=nil)
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Compute deximal approximation of algebraic real and complex roots.
# File examples/jas.rb 2021 def decimalRoots(a,eps=nil) 2022 if not a.is_a? RingElem 2023 a = RingElem.new(a); 2024 end 2025 return a.decimalRoots(eps); 2026 end
element(poly)
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Create an element from a string or an object.
# File examples/jas.rb 1857 def element(poly) 1858 if not poly.is_a? String 1859 begin 1860 if @ring == poly.ring 1861 return RingElem.new(poly); 1862 end 1863 rescue => e 1864 # pass 1865 end 1866 poly = str(poly); 1867 end 1868 i = SimIdeal.new( self, "( " + poly + " )" ); 1869 list = i.pset.list; 1870 if list.size > 0 1871 return RingElem.new( list[0] ); 1872 end 1873 end
factors(a)
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Compute irreducible factorization for modular, integer, rational number and algebriac number coefficients.
# File examples/jas.rb 1928 def factors(a) 1929 if a.is_a? RingElem 1930 a = a.elem; 1931 else 1932 a = element( a ); 1933 a = a.elem; 1934 end 1935 begin 1936 cf = @ring.coFac; 1937 if cf.is_a? GenPolynomialRing 1938 e = @factor.recursiveFactors( a ); 1939 else 1940 e = @factor.factors( a ); 1941 end 1942 ll = {}; 1943 for a in e.keySet() 1944 i = e.get(a); 1945 ll[ RingElem.new( a ) ] = i; 1946 end 1947 return ll; 1948 rescue => e 1949 puts "error " + str(e) 1950 return nil 1951 end 1952 end
factorsAbsolute(a)
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Compute absolute irreducible factorization for (modular,) rational number coefficients.
# File examples/jas.rb 1958 def factorsAbsolute(a) 1959 if a.is_a? RingElem 1960 a = a.elem; 1961 else 1962 a = element( a ); 1963 a = a.elem; 1964 end 1965 begin 1966 ll = @factor.factorsAbsolute( a ); 1967 ## ll = {}; 1968 ## for a in e.keySet() 1969 ## i = e.get(a); 1970 ## ll[ RingElem.new( a ) ] = i; 1971 return ll; 1972 rescue => e 1973 puts "error in factorsAbsolute " + str(e) 1974 return nil 1975 end 1976 end
gcd(a,b)
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Compute the greatest common divisor of a and b.
# File examples/jas.rb 1878 def gcd(a,b) 1879 if a.is_a? RingElem 1880 a = a.elem; 1881 else 1882 a = element( a ); 1883 a = a.elem; 1884 end 1885 if b.is_a? RingElem 1886 b = b.elem; 1887 else 1888 b = element( b ); 1889 b = b.elem; 1890 end 1891 cf = @ring.coFac; 1892 if cf.is_a? GenPolynomialRing 1893 e = @engine.recursiveGcd( a, b ); 1894 else 1895 e = @engine.gcd( a, b ); 1896 end 1897 return RingElem.new( e ); 1898 end
gens()
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Get list of generators of the polynomial ring.
# File examples/jas.rb 1823 def gens() 1824 ll = @ring.generators(); 1825 n = ll.map{ |e| RingElem.new(e) }; 1826 return n; 1827 end
ideal(ringstr="",list=nil)
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Create an ideal.
# File examples/jas.rb 1801 def ideal(ringstr="",list=nil) 1802 return JAS::SimIdeal.new(self,ringstr,list); 1803 end
inject_variables()
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Inject variables for generators in top level environment.
# File examples/jas.rb 1769 def inject_variables() 1770 begin 1771 require "irb/frame" # must be placed here 1772 bin = IRB::Frame.bottom(0); 1773 env = eval "self", bin; 1774 #puts "env = " + str(env) 1775 inject_gens(env) 1776 rescue => e 1777 puts "error: 'irb/frame' not found, e = " + str(e); 1778 end 1779 end
integrate(a)
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Integrate rational function or power series.
# File examples/jas.rb 2052 def integrate(a) 2053 if not a.is_a? RingElem 2054 a = RingElem.new(a); 2055 end 2056 return a.integrate(); 2057 end
one()
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Get the one of the polynomial ring.
# File examples/jas.rb 1832 def one() 1833 return RingElem.new( @ring.getONE() ); 1834 end
paramideal(ringstr="",list=nil,gbsys=nil)
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Create an ideal in a polynomial ring with parameter coefficients.
# File examples/jas.rb 1808 def paramideal(ringstr="",list=nil,gbsys=nil) 1809 return ParamIdeal.new(self,ringstr,list,gbsys); 1810 end
powerseriesRing()
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Get a power series ring from this ring.
# File examples/jas.rb 1815 def powerseriesRing() 1816 pr = MultiVarPowerSeriesRing.new(@ring); 1817 return MultiSeriesRing.new("",nil,pr); 1818 end
random(k=5,l=7,d=3,q=0.3)
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Get a random polynomial.
# File examples/jas.rb 1846 def random(k=5,l=7,d=3,q=0.3) 1847 r = @ring.random(k,l,d,q); 1848 if @ring.coFac.isField() 1849 r = r.monic(); 1850 end 1851 return RingElem.new( r ); 1852 end
realRoots(a,eps=nil)
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Compute real roots of univariate polynomial.
# File examples/jas.rb 1981 def realRoots(a,eps=nil) 1982 if not a.is_a? RingElem 1983 a = RingElem.new(a); 1984 end 1985 return a.realRoots(eps); 1986 end
rootReduce(a, b)
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Root reduce of real and complex algebraic numbers. Compute an extension field with a primitive element.
# File examples/jas.rb 2042 def rootReduce(a, b) 2043 if not a.is_a? RingElem 2044 a = RingElem.new(a); 2045 end 2046 return a.rootReduce(b); 2047 end
rootRefine(a,eps=nil)
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Compute algebraic real and complex roots refinement.
# File examples/jas.rb 2011 def rootRefine(a,eps=nil) 2012 if not a.is_a? RingElem 2013 a = RingElem.new(a); 2014 end 2015 return a.rootRefine(eps); 2016 end
rootsOfUnity(a)
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Roots of unity of real and complex algebraic numbers.
# File examples/jas.rb 2031 def rootsOfUnity(a) 2032 if not a.is_a? RingElem 2033 a = RingElem.new(a); 2034 end 2035 return a.rootsOfUnity(); 2036 end
squarefreeFactors(a)
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Compute squarefree factors of polynomial.
# File examples/jas.rb 1903 def squarefreeFactors(a) 1904 if a.is_a? RingElem 1905 a = a.elem; 1906 else 1907 a = element( a ); 1908 a = a.elem; 1909 end 1910 cf = @ring.coFac; 1911 if cf.is_a? GenPolynomialRing 1912 e = @sqf.recursiveSquarefreeFactors( a ); 1913 else 1914 e = @sqf.squarefreeFactors( a ); 1915 end 1916 ll = {}; 1917 for a in e.keySet() 1918 i = e.get(a); 1919 ll[ RingElem.new( a ) ] = i; 1920 end 1921 return ll; 1922 end
subring(polystr="", list=nil)
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Sub ring generators as Groebner base.
# File examples/jas.rb 2062 def subring(polystr="", list=nil) 2063 if list == nil 2064 sr = StringReader.new( polystr ); 2065 tok = GenPolynomialTokenizer.new(@ring,sr); 2066 @list = tok.nextPolynomialList(); 2067 else 2068 @list = rbarray2arraylist(list,rec=1); 2069 end 2070 sr = PolyGBUtil.subRing(@list); 2071 srr = sr.map { |a| RingElem.new(a) }; 2072 return srr; 2073 end
subringmember(list, a)
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Sub ring member test. list is a Groebner base. Test if a in K.
# File examples/jas.rb 2079 def subringmember(list, a) 2080 sr = list.map { |p| p.elem }; 2081 if a.is_a? RingElem 2082 a = a.elem; 2083 end 2084 b = PolyGBUtil.subRingMember(sr, a); 2085 return b; 2086 end
to_s()
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Create a string representation.
# File examples/jas.rb 1784 def to_s() 1785 return @ring.toScript(); 1786 end
variable_generators()
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Define instance variables for generators.
# File examples/jas.rb 1744 def variable_generators() 1745 Ring.instance_eval( "attr_accessor :generators;" ) 1746 @generators = {}; 1747 for i in self.gens() 1748 begin 1749 ivs = nameFromValue(i); 1750 if ivs != nil 1751 #puts "string: #{ivs} = " + ivs.class.to_s; 1752 if @generators[ ivs ] != nil 1753 puts "redefining local variable #{ivs}"; 1754 end 1755 @generators[ ivs ] = i; 1756 self.instance_eval( "def #{ivs}; @generators[ '#{ivs}' ]; end" ) 1757 end 1758 rescue => e 1759 puts "ring error: #{ivs} = " + i.to_s + ", e = " + str(e); 1760 #pass 1761 end 1762 end 1763 #puts "locally defined generators: " + @generators.keys().join(", "); 1764 end
zero()
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Get the zero of the polynomial ring.
# File examples/jas.rb 1839 def zero() 1840 return RingElem.new( @ring.getZERO() ); 1841 end