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 1950 def Ring.getEngineFactor(r) 1951 if r.is_a? RingElem 1952 r = r.elem; 1953 end 1954 if not r.is_a? GenPolynomialRing 1955 return nil; 1956 end 1957 begin 1958 i = FactorFactory.getImplementation(r.coFac); 1959 rescue => e 1960 i = nil 1961 end 1962 #puts "factor engine: #{i}"; 1963 return i; 1964 end
getEngineGcd(r)
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Get the polynomial gcd engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1907 def Ring.getEngineGcd(r) 1908 if r.is_a? RingElem 1909 r = r.elem; 1910 end 1911 if not r.is_a? GenPolynomialRing 1912 return nil; 1913 end 1914 begin 1915 i = GCDFactory.getProxy(r.coFac); 1916 #i = GCDFactory.getImplementation(r.coFac); 1917 rescue => e 1918 i = nil 1919 end 1920 #puts "gcd engine: #{i}"; 1921 return i; 1922 end
getEngineSqf(r)
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Get the polynomial squarefree engine implementation.
r is the given polynomial ring.
# File examples/jas.rb 1929 def Ring.getEngineSqf(r) 1930 if r.is_a? RingElem 1931 r = r.elem; 1932 end 1933 if not r.is_a? GenPolynomialRing 1934 return nil; 1935 end 1936 begin 1937 i = SquarefreeFactory.getImplementation(r.coFac); 1938 rescue => e 1939 i = nil 1940 end 1941 #puts "sqf engine: #{i}"; 1942 return i; 1943 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 1872 def initialize(ringstr="",ring=nil) 1873 if ring == nil 1874 sr = StringReader.new( ringstr ); 1875 tok = RingFactoryTokenizer.new(sr); 1876 pfac = tok.nextPolynomialRing(); 1877 #tok = GenPolynomialTokenizer.new(sr); 1878 #@pset = tok.nextPolynomialSet(); 1879 @ring = pfac; 1880 else 1881 if ring.is_a? Ring 1882 @ring = ring.ring 1883 else 1884 @ring = ring; 1885 end 1886 end 1887 # parameter ",fast=false" not possible w/o keyword params 1888 #if fast == true 1889 # return 1890 #end 1891 @engine = Ring.getEngineGcd(@ring); 1892 @sqf = Ring.getEngineSqf(@ring); 1893 @factor = Ring.getEngineFactor(@ring); 1894 variable_generators() 1895 #puts "self.class.auto_inject = " + self.class.auto_inject.to_s 1896 #puts "self.class.superclass.auto_inject = " + self.class.superclass.auto_inject.to_s 1897 if self.class.auto_inject or self.class.superclass.auto_inject # sic! 1898 inject_variables(); 1899 end 1900 end
Public Instance Methods
==(other)
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Test if two rings are equal.
# File examples/jas.rb 2017 def ==(other) 2018 if not other.is_a? Ring 2019 return false; 2020 end 2021 return @ring.equals(other.ring); 2022 end
CRT(polystr="", list=nil, rem=nil)
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Chinese remainder theorem.
# File examples/jas.rb 2317 def CRT(polystr="", list=nil, rem=nil) 2318 if list == nil 2319 sr = StringReader.new( polystr ); 2320 tok = GenPolynomialTokenizer.new(@ring,sr); 2321 @list = tok.nextPolynomialList(); 2322 else 2323 @list = rbarray2arraylist(list,nil,rec=2); 2324 end 2325 if rem == nil 2326 raise ArgumentError, "No remainders given." 2327 else 2328 @remlist = rbarray2arraylist(rem,nil,rec=1); 2329 end 2330 #puts "list = " + str(@list); 2331 #puts "remlist = " + str(@remlist); 2332 #puts 2333 h = PolyGBUtil.chineseRemainderTheorem(@list, @remlist); 2334 if h != nil 2335 h = RingElem.new(h); 2336 end 2337 return h; 2338 end
CRTinterpol(polystr="", list=nil, rem=nil)
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Chinese remainder theorem, interpolation.
# File examples/jas.rb 2343 def CRTinterpol(polystr="", list=nil, rem=nil) 2344 if list == nil 2345 sr = StringReader.new( polystr ); 2346 tok = GenPolynomialTokenizer.new(@ring,sr); 2347 @list = tok.nextPolynomialList(); 2348 else 2349 @list = rbarray2arraylist(list,nil,rec=2); 2350 end 2351 if rem == nil 2352 raise ArgumentError, "No remeinders given." 2353 else 2354 @remlist = rbarray2arraylist(rem,nil,rec=1); 2355 end 2356 #puts "ring = " + str(@ring.toScript()); 2357 #puts "list = " + str(@list); 2358 #puts "remlist = " + str(@remlist); 2359 #puts 2360 h = PolyGBUtil.CRTInterpolation(@ring, @list, @remlist); 2361 if h != nil 2362 h = RingElem.new(h); 2363 end 2364 return h; 2365 end
algebraicRoots(a,eps=nil)
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Compute algebraic real and complex roots of univariate polynomial.
# File examples/jas.rb 2227 def algebraicRoots(a,eps=nil) 2228 if not a.is_a? RingElem 2229 a = RingElem.new(a); 2230 end 2231 return a.algebraicRoots(eps); 2232 end
complexRoots(a,eps=nil)
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Compute complex roots of univariate polynomial.
# File examples/jas.rb 2217 def complexRoots(a,eps=nil) 2218 if not a.is_a? RingElem 2219 a = RingElem.new(a); 2220 end 2221 return a.complexRoots(eps); 2222 end
decimalRoots(a,eps=nil)
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Compute deximal approximation of algebraic real and complex roots.
# File examples/jas.rb 2247 def decimalRoots(a,eps=nil) 2248 if not a.is_a? RingElem 2249 a = RingElem.new(a); 2250 end 2251 return a.decimalRoots(eps); 2252 end
element(poly)
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Create an element from a string or an object.
# File examples/jas.rb 2083 def element(poly) 2084 if not poly.is_a? String 2085 begin 2086 if @ring == poly.ring 2087 return RingElem.new(poly); 2088 end 2089 rescue => e 2090 # pass 2091 end 2092 poly = str(poly); 2093 end 2094 i = SimIdeal.new( self, "( " + poly + " )" ); 2095 list = i.pset.list; 2096 if list.size > 0 2097 return RingElem.new( list[0] ); 2098 end 2099 end
factors(a)
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Compute irreducible factorization for modular, integer, rational number and algebriac number coefficients.
# File examples/jas.rb 2154 def factors(a) 2155 if a.is_a? RingElem 2156 a = a.elem; 2157 else 2158 a = element( a ); 2159 a = a.elem; 2160 end 2161 begin 2162 cf = @ring.coFac; 2163 if cf.is_a? GenPolynomialRing 2164 e = @factor.recursiveFactors( a ); 2165 else 2166 e = @factor.factors( a ); 2167 end 2168 ll = {}; 2169 for a in e.keySet() 2170 i = e.get(a); 2171 ll[ RingElem.new( a ) ] = i; 2172 end 2173 return ll; 2174 rescue => e 2175 puts "error " + str(e) 2176 return nil 2177 end 2178 end
factorsAbsolute(a)
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Compute absolute irreducible factorization for (modular,) rational number coefficients.
# File examples/jas.rb 2184 def factorsAbsolute(a) 2185 if a.is_a? RingElem 2186 a = a.elem; 2187 else 2188 a = element( a ); 2189 a = a.elem; 2190 end 2191 begin 2192 ll = @factor.factorsAbsolute( a ); 2193 ## ll = {}; 2194 ## for a in e.keySet() 2195 ## i = e.get(a); 2196 ## ll[ RingElem.new( a ) ] = i; 2197 return ll; 2198 rescue => e 2199 puts "error in factorsAbsolute " + str(e) 2200 return nil 2201 end 2202 end
gcd(a,b)
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Compute the greatest common divisor of a and b.
# File examples/jas.rb 2104 def gcd(a,b) 2105 if a.is_a? RingElem 2106 a = a.elem; 2107 else 2108 a = element( a ); 2109 a = a.elem; 2110 end 2111 if b.is_a? RingElem 2112 b = b.elem; 2113 else 2114 b = element( b ); 2115 b = b.elem; 2116 end 2117 cf = @ring.coFac; 2118 if cf.is_a? GenPolynomialRing 2119 e = @engine.recursiveGcd( a, b ); 2120 else 2121 e = @engine.gcd( a, b ); 2122 end 2123 return RingElem.new( e ); 2124 end
gens()
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Get list of generators of the polynomial ring.
# File examples/jas.rb 2049 def gens() 2050 ll = @ring.generators(); 2051 n = ll.map{ |e| RingElem.new(e) }; 2052 return n; 2053 end
ideal(ringstr="",list=nil)
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Create an ideal.
# File examples/jas.rb 2027 def ideal(ringstr="",list=nil) 2028 return JAS::SimIdeal.new(self,ringstr,list); 2029 end
inject_variables()
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Inject variables for generators in top level environment.
# File examples/jas.rb 1994 def inject_variables() 1995 begin 1996 require "irb/frame" # must be placed here 1997 bin = IRB::Frame.bottom(0); 1998 env = eval "self", bin; 1999 #puts "inject_gens: env1 = " + str(env) 2000 inject_gens(env) 2001 #puts "inject_gens: env2 = " + str(env) 2002 rescue => e 2003 puts "error: 'irb/frame' not found, e = " + str(e); 2004 end 2005 end
integrate(a)
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Integrate rational function or power series.
# File examples/jas.rb 2278 def integrate(a) 2279 if not a.is_a? RingElem 2280 a = RingElem.new(a); 2281 end 2282 return a.integrate(); 2283 end
one()
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Get the one of the polynomial ring.
# File examples/jas.rb 2058 def one() 2059 return RingElem.new( @ring.getONE() ); 2060 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 2034 def paramideal(ringstr="",list=nil,gbsys=nil) 2035 return ParamIdeal.new(self,ringstr,list,gbsys); 2036 end
powerseriesRing()
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Get a power series ring from this ring.
# File examples/jas.rb 2041 def powerseriesRing() 2042 pr = MultiVarPowerSeriesRing.new(@ring); 2043 return MultiSeriesRing.new("",nil,pr); 2044 end
random(k=5,l=7,d=3,q=0.3)
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Get a random polynomial.
# File examples/jas.rb 2072 def random(k=5,l=7,d=3,q=0.3) 2073 r = @ring.random(k,l,d,q); 2074 if @ring.coFac.isField() 2075 r = r.monic(); 2076 end 2077 return RingElem.new( r ); 2078 end
realRoots(a,eps=nil)
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Compute real roots of univariate polynomial.
# File examples/jas.rb 2207 def realRoots(a,eps=nil) 2208 if not a.is_a? RingElem 2209 a = RingElem.new(a); 2210 end 2211 return a.realRoots(eps); 2212 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 2268 def rootReduce(a, b) 2269 if not a.is_a? RingElem 2270 a = RingElem.new(a); 2271 end 2272 return a.rootReduce(b); 2273 end
rootRefine(a,eps=nil)
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Compute algebraic real and complex roots refinement.
# File examples/jas.rb 2237 def rootRefine(a,eps=nil) 2238 if not a.is_a? RingElem 2239 a = RingElem.new(a); 2240 end 2241 return a.rootRefine(eps); 2242 end
rootsOfUnity(a)
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Roots of unity of real and complex algebraic numbers.
# File examples/jas.rb 2257 def rootsOfUnity(a) 2258 if not a.is_a? RingElem 2259 a = RingElem.new(a); 2260 end 2261 return a.rootsOfUnity(); 2262 end
squarefreeFactors(a)
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Compute squarefree factors of polynomial.
# File examples/jas.rb 2129 def squarefreeFactors(a) 2130 if a.is_a? RingElem 2131 a = a.elem; 2132 else 2133 a = element( a ); 2134 a = a.elem; 2135 end 2136 cf = @ring.coFac; 2137 if cf.is_a? GenPolynomialRing 2138 e = @sqf.recursiveSquarefreeFactors( a ); 2139 else 2140 e = @sqf.squarefreeFactors( a ); 2141 end 2142 ll = {}; 2143 for a in e.keySet() 2144 i = e.get(a); 2145 ll[ RingElem.new( a ) ] = i; 2146 end 2147 return ll; 2148 end
subring(polystr="", list=nil)
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Sub ring generators as Groebner base.
# File examples/jas.rb 2288 def subring(polystr="", list=nil) 2289 if list == nil 2290 sr = StringReader.new( polystr ); 2291 tok = GenPolynomialTokenizer.new(@ring,sr); 2292 @list = tok.nextPolynomialList(); 2293 else 2294 @list = rbarray2arraylist(list,rec=1); 2295 end 2296 sr = PolyGBUtil.subRing(@list); 2297 srr = sr.map { |a| RingElem.new(a) }; 2298 return srr; 2299 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 2305 def subringmember(list, a) 2306 sr = list.map { |p| p.elem }; 2307 if a.is_a? RingElem 2308 a = a.elem; 2309 end 2310 b = PolyGBUtil.subRingMember(sr, a); 2311 return b; 2312 end
to_s()
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Create a string representation.
# File examples/jas.rb 2010 def to_s() 2011 return @ring.toScript(); 2012 end
variable_generators()
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Define instance variables for generators.
# File examples/jas.rb 1969 def variable_generators() 1970 Ring.instance_eval( "attr_accessor :generators;" ) 1971 @generators = {}; 1972 for i in self.gens() 1973 begin 1974 ivs = nameFromValue(i); 1975 if ivs != nil 1976 #puts "string: #{ivs} = " + ivs.class.to_s; 1977 if @generators[ ivs ] != nil 1978 puts "redefining local variable #{ivs}"; 1979 end 1980 @generators[ ivs ] = i; 1981 self.instance_eval( "def #{ivs}; @generators[ '#{ivs}' ]; end" ) 1982 end 1983 rescue => e 1984 puts "ring error: #{ivs} = " + i.to_s + ", e = " + str(e); 1985 #pass 1986 end 1987 end 1988 #puts "locally defined generators: " + @generators.keys().join(", "); 1989 end
zero()
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Get the zero of the polynomial ring.
# File examples/jas.rb 2065 def zero() 2066 return RingElem.new( @ring.getZERO() ); 2067 end