September 2017 Update

Task/Formal-power-series/Zkl/formal-power-series-1.zkl

@@ -0,0 +1,29 @@
+class IPS{
+   var [protected] w;   // the coefficients of the infinite series
+   fcn init(w_or_a,b,c,etc){  // IPS(1,2,3) --> (1,2,3,0,0,...)
+      switch [arglist]{
+	 case(Walker)		{ w=w_or_a.tweak(Void,0) }
+	 else			{ w=vm.arglist.walker().tweak(Void,0) }
+      }
+   }
+   fcn __opAdd(ipf){   //IPS(1,2,3)+IPS(4,5)-->IPS(5,6,3,0,...), returns modified self
+      switch[arglist]{
+         case(1){ addConst(ipf) }         // IPS + int/float
+	 else   { w=w.zipWith('+,ipf.w) } // IPS + IPS
+      }
+      self
+   }
+   fcn __opSub(ipf){ w=w.zipWith('-,ipf.w); self } // IPS - IPSHaskell
+   fcn __opMul(ipf){ }  // stub
+   fcn __opDiv(x){ w.next().toFloat()/x } // *IPS/x, for integtate()
+   fcn __opNegate  { w=w.tweak(Op("--")); self }
+   // integtate: b0 = 0 by convention, bn = an-1/n
+   fcn integrate{ w=w.zipWith('/,[1..]).push(0.0); self }
+   fcn diff     { w=w.zipWith('*,[1..]); 	   self }
+   fcn facts{ (1).walker(*).tweak(fcn(n){ (1).reduce(n,'*,1) }) } // 1!,2!...
+   fcn walk(n){ w.walk(n) }
+   fcn value(x,N=15){ ns:=[1..]; w.reduce(N,'wrap(s,an){ s + an*x.pow(ns.next()) }) }
+   fcn cons(k){ w.push(k); self }  //--> k, a0, a1, a2, ...
+   // addConst(k) --> k + a0, a1, a2, ..., same as k + IPS
+   fcn addConst(k){ (w.next() + k) : w.push(_); self }
+}

Task/Formal-power-series/Zkl/formal-power-series-2.zkl

@@ -0,0 +1,2 @@
+(IPS(1,2,3) + IPS(4,5)).walk(5).println();
+(-IPS([1..]) + 11).walk(5).println();

Task/Formal-power-series/Zkl/formal-power-series-3.zkl

@@ -0,0 +1,17 @@
+fcn sine{  // sine Taylor series: 0 + x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - ...
+   IPS(Utils.Helpers.cycle(1.0, 0.0, -1.0, 0.0).zipWith('/,IPS.facts()))
+   .cons(0.0)
+}
+print("Sine Taylor series: "); dostuff(sine,"sin");
+
+fcn cosine{ -sine().integrate() + 1.0 }
+print("Cosine power series: "); dostuff(cosine,"cos");
+
+fcn dostuff(ips,name){  // print series, evaluate at various points
+   f:='wrap(x,xnm){ v:=ips().value(x);
+      println("%s(%s) \U2192; %f  \U394;=%f".fmt(name,xnm,v,x.Method(name)()-v));
+   };
+   ips().walk(15).println();
+   f(0.0,"0"); f((1.0).pi/4,"\Ubc;\U3c0;");
+   f((1.0).pi/2,"\Ubd;\U3c0;"); f((1.0).pi,"\U3c0;");
+}