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 1912 def Ring.getEngineFactor(r) 1913 if r.is_a? RingElem 1914 r = r.elem; 1915 end 1916 if not r.is_a? GenPolynomialRing 1917 return nil; 1918 end 1919 begin 1920 i = FactorFactory.getImplementation(r.coFac); 1921 rescue => e 1922 i = nil 1923 end 1924 #puts "factor engine: #{i}"; 1925 return i; 1926 end
getEngineGcd(r)
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Get the polynomial gcd engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1869 def Ring.getEngineGcd(r) 1870 if r.is_a? RingElem 1871 r = r.elem; 1872 end 1873 if not r.is_a? GenPolynomialRing 1874 return nil; 1875 end 1876 begin 1877 i = GCDFactory.getProxy(r.coFac); 1878 #i = GCDFactory.getImplementation(r.coFac); 1879 rescue => e 1880 i = nil 1881 end 1882 #puts "gcd engine: #{i}"; 1883 return i; 1884 end
getEngineSqf(r)
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Get the polynomial squarefree engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1891 def Ring.getEngineSqf(r) 1892 if r.is_a? RingElem 1893 r = r.elem; 1894 end 1895 if not r.is_a? GenPolynomialRing 1896 return nil; 1897 end 1898 begin 1899 i = SquarefreeFactory.getImplementation(r.coFac); 1900 rescue => e 1901 i = nil 1902 end 1903 #puts "sqf engine: #{i}"; 1904 return i; 1905 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 1836 def initialize(ringstr="",ring=nil) 1837 if ring == nil 1838 sr = StringReader.new( ringstr ); 1839 tok = RingFactoryTokenizer.new(sr); 1840 pfac = tok.nextPolynomialRing(); 1841 #tok = GenPolynomialTokenizer.new(sr); 1842 #@pset = tok.nextPolynomialSet(); 1843 @ring = pfac; 1844 else 1845 if ring.is_a? Ring 1846 @ring = ring.ring 1847 else 1848 @ring = ring; 1849 end 1850 end 1851 # parameter ",fast=false" not possible w/o keyword params 1852 #if fast == true 1853 # return 1854 #end 1855 @engine = Ring.getEngineGcd(@ring); 1856 @sqf = Ring.getEngineSqf(@ring); 1857 @factor = Ring.getEngineFactor(@ring); 1858 variable_generators() 1859 if self.class.auto_inject or self.class.superclass.auto_inject # sic! 1860 inject_variables(); 1861 end 1862 end
Public Instance Methods
==(other)
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Test if two rings are equal.
# File examples/jas.rb 1978 def ==(other) 1979 if not other.is_a? Ring 1980 return false; 1981 end 1982 return @ring.equals(other.ring); 1983 end
CRT(polystr="", list=nil, rem=nil)
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Chinese remainder theorem.
# File examples/jas.rb 2278 def CRT(polystr="", list=nil, rem=nil) 2279 if list == nil 2280 sr = StringReader.new( polystr ); 2281 tok = GenPolynomialTokenizer.new(@ring,sr); 2282 @list = tok.nextPolynomialList(); 2283 else 2284 @list = rbarray2arraylist(list,nil,rec=2); 2285 end 2286 if rem == nil 2287 raise ArgumentError, "No remainders given." 2288 else 2289 @remlist = rbarray2arraylist(rem,nil,rec=1); 2290 end 2291 #puts "list = " + str(@list); 2292 #puts "remlist = " + str(@remlist); 2293 #puts 2294 h = PolyGBUtil.chineseRemainderTheorem(@list, @remlist); 2295 if h != nil 2296 h = RingElem.new(h); 2297 end 2298 return h; 2299 end
CRTinterpol(polystr="", list=nil, rem=nil)
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Chinese remainder theorem, interpolation.
# File examples/jas.rb 2304 def CRTinterpol(polystr="", list=nil, rem=nil) 2305 if list == nil 2306 sr = StringReader.new( polystr ); 2307 tok = GenPolynomialTokenizer.new(@ring,sr); 2308 @list = tok.nextPolynomialList(); 2309 else 2310 @list = rbarray2arraylist(list,nil,rec=2); 2311 end 2312 if rem == nil 2313 raise ArgumentError, "No remeinders given." 2314 else 2315 @remlist = rbarray2arraylist(rem,nil,rec=1); 2316 end 2317 #puts "ring = " + str(@ring.toScript()); 2318 #puts "list = " + str(@list); 2319 #puts "remlist = " + str(@remlist); 2320 #puts 2321 h = PolyGBUtil.CRTInterpolation(@ring, @list, @remlist); 2322 if h != nil 2323 h = RingElem.new(h); 2324 end 2325 return h; 2326 end
algebraicRoots(a,eps=nil)
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Compute algebraic real and complex roots of univariate polynomial.
# File examples/jas.rb 2188 def algebraicRoots(a,eps=nil) 2189 if not a.is_a? RingElem 2190 a = RingElem.new(a); 2191 end 2192 return a.algebraicRoots(eps); 2193 end
complexRoots(a,eps=nil)
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Compute complex roots of univariate polynomial.
# File examples/jas.rb 2178 def complexRoots(a,eps=nil) 2179 if not a.is_a? RingElem 2180 a = RingElem.new(a); 2181 end 2182 return a.complexRoots(eps); 2183 end
decimalRoots(a,eps=nil)
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Compute deximal approximation of algebraic real and complex roots.
# File examples/jas.rb 2208 def decimalRoots(a,eps=nil) 2209 if not a.is_a? RingElem 2210 a = RingElem.new(a); 2211 end 2212 return a.decimalRoots(eps); 2213 end
element(poly)
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Create an element from a string or an object.
# File examples/jas.rb 2044 def element(poly) 2045 if not poly.is_a? String 2046 begin 2047 if @ring == poly.ring 2048 return RingElem.new(poly); 2049 end 2050 rescue => e 2051 # pass 2052 end 2053 poly = str(poly); 2054 end 2055 i = SimIdeal.new( self, "( " + poly + " )" ); 2056 list = i.pset.list; 2057 if list.size > 0 2058 return RingElem.new( list[0] ); 2059 end 2060 end
factors(a)
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Compute irreducible factorization for modular, integer, rational number and algebriac number coefficients.
# File examples/jas.rb 2115 def factors(a) 2116 if a.is_a? RingElem 2117 a = a.elem; 2118 else 2119 a = element( a ); 2120 a = a.elem; 2121 end 2122 begin 2123 cf = @ring.coFac; 2124 if cf.is_a? GenPolynomialRing 2125 e = @factor.recursiveFactors( a ); 2126 else 2127 e = @factor.factors( a ); 2128 end 2129 ll = {}; 2130 for a in e.keySet() 2131 i = e.get(a); 2132 ll[ RingElem.new( a ) ] = i; 2133 end 2134 return ll; 2135 rescue => e 2136 puts "error " + str(e) 2137 return nil 2138 end 2139 end
factorsAbsolute(a)
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Compute absolute irreducible factorization for (modular,) rational number coefficients.
# File examples/jas.rb 2145 def factorsAbsolute(a) 2146 if a.is_a? RingElem 2147 a = a.elem; 2148 else 2149 a = element( a ); 2150 a = a.elem; 2151 end 2152 begin 2153 ll = @factor.factorsAbsolute( a ); 2154 ## ll = {}; 2155 ## for a in e.keySet() 2156 ## i = e.get(a); 2157 ## ll[ RingElem.new( a ) ] = i; 2158 return ll; 2159 rescue => e 2160 puts "error in factorsAbsolute " + str(e) 2161 return nil 2162 end 2163 end
gcd(a,b)
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Compute the greatest common divisor of a and b.
# File examples/jas.rb 2065 def gcd(a,b) 2066 if a.is_a? RingElem 2067 a = a.elem; 2068 else 2069 a = element( a ); 2070 a = a.elem; 2071 end 2072 if b.is_a? RingElem 2073 b = b.elem; 2074 else 2075 b = element( b ); 2076 b = b.elem; 2077 end 2078 cf = @ring.coFac; 2079 if cf.is_a? GenPolynomialRing 2080 e = @engine.recursiveGcd( a, b ); 2081 else 2082 e = @engine.gcd( a, b ); 2083 end 2084 return RingElem.new( e ); 2085 end
gens()
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Get list of generators of the polynomial ring.
# File examples/jas.rb 2010 def gens() 2011 ll = @ring.generators(); 2012 n = ll.map{ |e| RingElem.new(e) }; 2013 return n; 2014 end
ideal(ringstr="",list=nil)
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Create an ideal.
# File examples/jas.rb 1988 def ideal(ringstr="",list=nil) 1989 return JAS::SimIdeal.new(self,ringstr,list); 1990 end
inject_variables()
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Inject variables for generators in top level environment.
# File examples/jas.rb 1956 def inject_variables() 1957 begin 1958 require "irb/frame" # must be placed here 1959 bin = IRB::Frame.bottom(0); 1960 env = eval "self", bin; 1961 #puts "env = " + str(env) 1962 inject_gens(env) 1963 rescue => e 1964 puts "error: 'irb/frame' not found, e = " + str(e); 1965 end 1966 end
integrate(a)
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Integrate rational function or power series.
# File examples/jas.rb 2239 def integrate(a) 2240 if not a.is_a? RingElem 2241 a = RingElem.new(a); 2242 end 2243 return a.integrate(); 2244 end
one()
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Get the one of the polynomial ring.
# File examples/jas.rb 2019 def one() 2020 return RingElem.new( @ring.getONE() ); 2021 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 1995 def paramideal(ringstr="",list=nil,gbsys=nil) 1996 return ParamIdeal.new(self,ringstr,list,gbsys); 1997 end
powerseriesRing()
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Get a power series ring from this ring.
# File examples/jas.rb 2002 def powerseriesRing() 2003 pr = MultiVarPowerSeriesRing.new(@ring); 2004 return MultiSeriesRing.new("",nil,pr); 2005 end
random(k=5,l=7,d=3,q=0.3)
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Get a random polynomial.
# File examples/jas.rb 2033 def random(k=5,l=7,d=3,q=0.3) 2034 r = @ring.random(k,l,d,q); 2035 if @ring.coFac.isField() 2036 r = r.monic(); 2037 end 2038 return RingElem.new( r ); 2039 end
realRoots(a,eps=nil)
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Compute real roots of univariate polynomial.
# File examples/jas.rb 2168 def realRoots(a,eps=nil) 2169 if not a.is_a? RingElem 2170 a = RingElem.new(a); 2171 end 2172 return a.realRoots(eps); 2173 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 2229 def rootReduce(a, b) 2230 if not a.is_a? RingElem 2231 a = RingElem.new(a); 2232 end 2233 return a.rootReduce(b); 2234 end
rootRefine(a,eps=nil)
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Compute algebraic real and complex roots refinement.
# File examples/jas.rb 2198 def rootRefine(a,eps=nil) 2199 if not a.is_a? RingElem 2200 a = RingElem.new(a); 2201 end 2202 return a.rootRefine(eps); 2203 end
rootsOfUnity(a)
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Roots of unity of real and complex algebraic numbers.
# File examples/jas.rb 2218 def rootsOfUnity(a) 2219 if not a.is_a? RingElem 2220 a = RingElem.new(a); 2221 end 2222 return a.rootsOfUnity(); 2223 end
squarefreeFactors(a)
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Compute squarefree factors of polynomial.
# File examples/jas.rb 2090 def squarefreeFactors(a) 2091 if a.is_a? RingElem 2092 a = a.elem; 2093 else 2094 a = element( a ); 2095 a = a.elem; 2096 end 2097 cf = @ring.coFac; 2098 if cf.is_a? GenPolynomialRing 2099 e = @sqf.recursiveSquarefreeFactors( a ); 2100 else 2101 e = @sqf.squarefreeFactors( a ); 2102 end 2103 ll = {}; 2104 for a in e.keySet() 2105 i = e.get(a); 2106 ll[ RingElem.new( a ) ] = i; 2107 end 2108 return ll; 2109 end
subring(polystr="", list=nil)
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Sub ring generators as Groebner base.
# File examples/jas.rb 2249 def subring(polystr="", list=nil) 2250 if list == nil 2251 sr = StringReader.new( polystr ); 2252 tok = GenPolynomialTokenizer.new(@ring,sr); 2253 @list = tok.nextPolynomialList(); 2254 else 2255 @list = rbarray2arraylist(list,rec=1); 2256 end 2257 sr = PolyGBUtil.subRing(@list); 2258 srr = sr.map { |a| RingElem.new(a) }; 2259 return srr; 2260 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 2266 def subringmember(list, a) 2267 sr = list.map { |p| p.elem }; 2268 if a.is_a? RingElem 2269 a = a.elem; 2270 end 2271 b = PolyGBUtil.subRingMember(sr, a); 2272 return b; 2273 end
to_s()
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Create a string representation.
# File examples/jas.rb 1971 def to_s() 1972 return @ring.toScript(); 1973 end
variable_generators()
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Define instance variables for generators.
# File examples/jas.rb 1931 def variable_generators() 1932 Ring.instance_eval( "attr_accessor :generators;" ) 1933 @generators = {}; 1934 for i in self.gens() 1935 begin 1936 ivs = nameFromValue(i); 1937 if ivs != nil 1938 #puts "string: #{ivs} = " + ivs.class.to_s; 1939 if @generators[ ivs ] != nil 1940 puts "redefining local variable #{ivs}"; 1941 end 1942 @generators[ ivs ] = i; 1943 self.instance_eval( "def #{ivs}; @generators[ '#{ivs}' ]; end" ) 1944 end 1945 rescue => e 1946 puts "ring error: #{ivs} = " + i.to_s + ", e = " + str(e); 1947 #pass 1948 end 1949 end 1950 #puts "locally defined generators: " + @generators.keys().join(", "); 1951 end
zero()
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Get the zero of the polynomial ring.
# File examples/jas.rb 2026 def zero() 2027 return RingElem.new( @ring.getZERO() ); 2028 end