【SEOテキスト】宇田雄一「古典物理学」V12の定義:∀A1∈N01(N01);∀A3∈R+(R+);∀A4∈R(R);∀n∈N;∀p∈Pn;V12(A1,A3,A4,p)∈F12(F12)and【1】and【2】and【3】【1】[V12(A1,A3,A4,p)](0)=0【2】∀m∈N;∀f∈F12,m;m≠n⇒[V12(A1,A3,A4,p)](f)=[V12(A1,A3,A4,1∈Pm)](f)【3】∀f∈F12,n;[V12(A1,A3,A4,p)](f)∈F12,n
and【3a】and【3b】【3a】[[V12(A1,A3,A4,p)](f)](N2,n)=[V2,n(A1,p)](f(N2,n))【3b】∀i∈2;∀k∈{1,・・・,n};[[V12(A1,A3,A4,p)](f)](i,p(k))=Ai+2(f(i,k)),V14の定義:∀A1∈N01(N01);∀A2∈F3(F3);∀A3∈R+(R+);∀A4∈R(R);∀n∈N;∀p∈Pn;V14(A1,A2,A3,A4,p)∈F14(F14)and【1】and【2】【1】∀f∈F3;[V14(A1,A2,A3,A4,p)](f)=[V3(A1,A2)](f)【2】∀m∈N;∀f∈F14,m;[V14(A1,A2,A3,A4,p)](f)∈F14,m
and[[V14(A1,A2,A3,A4,p)](f)](N12,m)=[V12(A1,A3,A4,p)](f(N12,m))and[[V14(A1,A2,A3,A4,p)](f)](N3)=[V3(A1,A2)](f(N3)),V01の定義:∀A1∈N01(N01);V01(A1)∈F01(F01)and∀f∈F01;∀ξ∈N01;[[V01(A1)](f)](A1(ξ))=f(ξ),V02,nの定義:∀A1∈N01(N01);∀n∈N;∀p∈Pn;V02,n(A1,p)∈F02,n(F02,n)and∀f∈F02,n;∀k∈{1,・・・,n};[[V02,n(A1,p)](f)](□,p(k),3)=[V01(A1)](f(□,k,3)),V04,nの定義:∀A1∈N01(N01);∀A2∈F3(F3);∀n∈N;∀p∈Pn;V04,n(A1,A2,p)∈F04,n(F04,n)and∀f∈F04,n;【1】and【2】【1】[[V04,n(A1,A2,p)](f)](N02,n)=[V02,n(A1,p)](f(N02,n))【2】[[V04,n(A1,A2,p)](f)](N3)=[V3(A1,A2)](f(N3)),V22の定義:∀A1∈N01(N01);∀A3∈R+(R+);∀A4∈R(R);V22(A1,A3,A4)∈F22(F22)and∀f∈F22;∀(ξ,i,3)∈N22;[[V22(A1,A3,A4)](f)](A1(ξ),i,3)=Ai+2(f(ξ,i,3))
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