Changes between Version 47 and Version 48 of PolynomialExpansion

Timestamp:

01/26/16 20:34:17 (10 years ago)

Author:

sili

Comment:

--

PolynomialExpansion

@@ -13 +13 @@
   alpha,,0,, = (b,,0,,^2^+b,,1,,^2^) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))
 
-Step 3: r,,1,, = r,,0,, - alpha,,0,,  Ap,,0,,  ('''No expansion''')
+Step 3: r,,1,, = r,,0,, - alpha,,0,,*Ap,,0,,  ('''No expansion''')
   r[0] = (b,,0,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,0,,b,,0,,+a,,1,,b,,1,,)) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))
 
   r[1] = (b,,1,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,1,,b,,0,,+a,,2,,b,,1,,)) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))
 
-Step 4: x,,1,, = x,,0,, + alphap,,0,,  ('''No expansion''')
+Step 4: x,,1,, = x,,0,, + alpha,,0,,*p,,0,,  ('''No expansion''')
   x[0] = (b,,0,,(b,,0,,^2^ + b,,1,,^2^)) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))
 
   x[1] = (b,,1,,(b,,0,,^2^ + b,,1,,^2^)) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))
 
-Step 5: beta = rsnew / rsold = <r,,1,,, r,,1,,> / <r,,0,,, r,,0,,>
+Step 5: beta = rsnew / rsold = <r,,1,,, r,,1,,> / <r,,0,,, r,,0,,>  ('''No expansion''')
   rsnew = ((b,,0,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,0,,b,,0,,+a,,1,,b,,1,,))^2^ + (b,,1,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,1,,b,,0,,+a,,2,,b,,1,,))^2^) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))^2^
 
   beta = ((b,,0,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,0,,b,,0,,+a,,1,,b,,1,,))^2^ + (b,,1,,(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)) - (b,,0,,^2^+b,,1,,^2^)(a,,1,,b,,0,,+a,,2,,b,,1,,))^2^) / (b,,0,,^2^+b,,1,,^2^)(b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))^2^
 
-Step 6: p,,1,, = r,,1,, +beta  p,,0,,
+Step 6: p,,1,, = r,,1,, +beta*p,,0,,
   p[0] = (-1)((a,,1,,b,,0,, + a,,2,,b,,1,,)(b,,0,,^2^ + b,,1,,^2^)(-a,,1,,b,,0,,^2^ + a,,0,,b,,0,,b,,1,, - a,,2,,b,,0,,b,,1,, + a,,1,,b,,1,,^2^)) / (b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,))^2^
 
@@ -38 +38 @@
   alpha,,1,, = (a,,0,,b,,0,,^2^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^) / ((-a,,1,,^2^ + a,,0,,a,,2,,) (b,,0,,^2^ + b,,1,,^2^))
 
-Step 8: r,,2,, = r,,1,, - alpha,,1,,  Ap,,1,,
+Step 8: r,,2,, = r,,1,, - alpha,,1,,*Ap,,1,,
   r[0] = 0
 
   r[1] = 0
 
-Step 9: x,,2,, = x,,1,, + alpha,,1,,p,,1,,
+Step 9: x,,2,, = x,,1,, + alpha,,1,,*p,,1,,
   x[0] = (a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^)
 
@@ -49 +49 @@
 
 assertion:  
-  bncg[0] = A[0][0]x[0] + A[0][1]x[1] = a,,0,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,1,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,
+  bncg[0] = A[0][0]*x[0] + A[0][1]*x[1] = a,,0,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,1,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,
 
-  bncg[1] = A[1][0]x[0] + A[1][1]x[1] = a,,1,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,2,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,
+  bncg[1] = A[1][0]*x[0] + A[1][1]*x[1] = a,,1,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,2,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,
 
   b[0] = b,,0,,