"""Sample the analytic jet-transport formulas of Example 4.29 into editable SVG.""" from pathlib import Path from math import exp def points(fun,ymin,ymax,top,height): result=[] for i in range(481): w=-1.2+2.4*i/480 px=630+500*(w+1.2)/2.4 py=top+height*(ymax-fun(w))/(ymax-ymin) result.append(f'{px:.5f},{py:.5f}') return ' '.join(result) slope=points(lambda w:exp(-w*w),0,1.1,170,235) second=points(lambda w:-2*w*exp(-2*w*w),-.7,.7,512,230) svg=f''' Formal transport and one finite coefficient domain For H prime exp(u squared), source u=0 and slope p0=1 are transported to u=w, slope exp(-w squared), and second derivative f(w)=-2w exp(-2w squared). The plots sample w from -1.2 to 1.2 in 481 points. The formal series f has zero constant term and nonzero linear coefficient -2. The coefficient map therefore extends to a fraction field when p0 is nonzero. Formal transport and a finite source-slope domain H′(u)=exp(u²), H(U)=H(u)+H(w), source a=(0,0). Coefficient selection and transport back u=0, slope p₀ Fixed-fibre coordinate algebra Rₗ gw u=w, p=exp(−w²)p₀ f(w,p₀)=−2w exp(−2w²)p₀² [w]f=−2p₀² ≠ 0 on p₀ ≠ 0 ordinary coefficient map A[f⁻¹] → Frac(L[[w]]) Nonzero series are invertible in the field. gw⁻¹ and field faithfulness Ranks and symbol identities at the original jet One finite source-slope restriction: p₀ ≠ 0. Analytic values when p₀=1 p(w)=exp(−w²) 00.510.70−0.7 −1.201.2−1.201.2 ww f(w,1)=−2w exp(−2w²) f(0,1)=0 [w]f=−2 481 samples of each displayed analytic formula. ''' if __name__=='__main__': Path(__file__).with_suffix('.svg').write_text(svg,encoding='utf-8',newline='\n')