Notation by work

AddMul Arithmetic Reconstruction

All notation · Glossary · Source coverage

69 symbol spellings in 16 mathematical passages across 2 selected source files. Subscripts and superscripts have their own entries alongside their base symbols.

The same symbol can have several meanings here. A passage classified as a definition may define another part of its expression. Read the linked context before assigning a meaning.

All 69 entries are available below.

+Use in source · 11 passages

Search aliases: +

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

=Use in source · 13 passages

Search aliases: =

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

AUse in source · 2 passages

Search aliases: A

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

aUse in source · 2 passages

Search aliases: a

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

a_jUse in source · 2 passages

Search aliases: a_j

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

BUse in source · 3 passages

Search aliases: B

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

\bmodUse in source · 2 passages

Search aliases: bmod

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

CUse in source · 4 passages

Search aliases: C

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Use in source · RESEARCH_NOTE.md, line 130
C_p,N(x,y)=fract_N(x)+t_N(y)-t_N(x+y)p pmod p^N-1,
Exact mathematical passage
```
C_{p,N}(x,y)=\frac{t_N(x)+t_N(y)-t_N(x+y)}p \quad\pmod {p^{N-1}},
```

C_{p,N}Use in source · 3 passages

Search aliases: C_p,N

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Use in source · RESEARCH_NOTE.md, line 130
C_p,N(x,y)=fract_N(x)+t_N(y)-t_N(x+y)p pmod p^N-1,
Exact mathematical passage
```
C_{p,N}(x,y)=\frac{t_N(x)+t_N(y)-t_N(x+y)}p \quad\pmod {p^{N-1}},
```

dUse in source · 3 passages

Search aliases: d

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

EUse in source · 3 passages

Search aliases: E

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Use in source · RESEARCH_NOTE.md, line 56
E≥fracq^k(q^L-1)(q^L-p^L)2(p^L+1).tag1
Exact mathematical passage
```
\boxed{E\ge\frac{q^k(q^L-1)(q^L-p^L)}{2(p^L+1)}.}\tag{1}
```

eUse in source · 1 passage

Search aliases: e

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

e_kUse in source · 1 passage

Search aliases: e_k

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

E_{s,d,k}^{\mathrm{sharp}}Use in source · 1 passage

Search aliases: E_s,d,k^sharp mathrm

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Use in source · RESEARCH_NOTE.md, line 111
E_s,d,k^sharp= fracq^k(q^s-p^s)(q^s-1)^d+12^d+1(p^s+1).tag3
Exact mathematical passage
```
\boxed{ E_{s,d,k}^{\mathrm{sharp}}=
\frac{q^k(q^s-p^s)(q^s-1)^{d+1}}{2^{d+1}(p^s+1)}.}\tag{3}
```

FUse in source · 2 passages

Search aliases: F

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

iUse in source · 1 passage

Search aliases: i

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Use in source · RESEARCH_NOTE.md, line 150
∑_i=0^p-1 C_p,N(1,i)≡ 1pmodp^N-1
Exact mathematical passage
```
\boxed{\sum_{i=0}^{p-1} C_{p,N}(1,i)\equiv 1\pmod{p^{N-1}}}
```

jUse in source · 4 passages

Search aliases: j

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Use in source · RESEARCH_NOTE.md, line 36
p^k+jL≡ p^kpmod M.
Exact mathematical passage
```
p^{k+jL}\equiv p^k\pmod M.
```

kUse in source · 6 passages

Search aliases: k

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

LUse in source · 2 passages

Search aliases: L

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Use in source · RESEARCH_NOTE.md, line 36
p^k+jL≡ p^kpmod M.
Exact mathematical passage
```
p^{k+jL}\equiv p^k\pmod M.
```

MUse in source · 3 passages

Search aliases: M

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

\mathscrUse in source · 1 passage

Search aliases: mathscr

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

\maxUse in source · 1 passage

Search aliases: max

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Use in source · RESEARCH_NOTE.md, line 92
max_0≤ j≤ d+1|r_k+j|≥ fracq^k|q-p||P(q)|∑_j=0^d+1|a_j|. tag2
Exact mathematical passage
```
\boxed{
\max_{0\le j\le d+1}|r_{k+j}|\ge
\frac{q^k|q-p||P(q)|}{\sum_{j=0}^{d+1}|a_j|}.
}\tag{2}
```

\max_{0\le j\le d+1}Use in source · 1 passage

Search aliases: max_0≤ j≤ d+1 max le le

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Use in source · RESEARCH_NOTE.md, line 92
max_0≤ j≤ d+1|r_k+j|≥ fracq^k|q-p||P(q)|∑_j=0^d+1|a_j|. tag2
Exact mathematical passage
```
\boxed{
\max_{0\le j\le d+1}|r_{k+j}|\ge
\frac{q^k|q-p||P(q)|}{\sum_{j=0}^{d+1}|a_j|}.
}\tag{2}
```

NUse in source · 5 passages

Search aliases: N

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

nUse in source · 1 passage

Search aliases: n

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

PUse in source · 3 passages

Search aliases: P

Link to this entry ·

Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

pUse in source · 12 passages

Search aliases: p

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

p^kUse in source · 2 passages

Search aliases: p^k

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

p^{k+jL}Use in source · 1 passage

Search aliases: p^k+jL

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Use in source · RESEARCH_NOTE.md, line 36
p^k+jL≡ p^kpmod M.
Exact mathematical passage
```
p^{k+jL}\equiv p^k\pmod M.
```

p^LUse in source · 1 passage

Search aliases: p^L

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Use in source · RESEARCH_NOTE.md, line 56
E≥fracq^k(q^L-1)(q^L-p^L)2(p^L+1).tag1
Exact mathematical passage
```
\boxed{E\ge\frac{q^k(q^L-1)(q^L-p^L)}{2(p^L+1)}.}\tag{1}
```

p^NUse in source · 2 passages

Search aliases: p^N

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

p^{N-1}Use in source · 4 passages

Search aliases: p^N-1

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

p^sUse in source · 1 passage

Search aliases: p^s

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Use in source · RESEARCH_NOTE.md, line 111
E_s,d,k^sharp= fracq^k(q^s-p^s)(q^s-1)^d+12^d+1(p^s+1).tag3
Exact mathematical passage
```
\boxed{ E_{s,d,k}^{\mathrm{sharp}}=
\frac{q^k(q^s-p^s)(q^s-1)^{d+1}}{2^{d+1}(p^s+1)}.}\tag{3}
```

\pmodUse in source · 6 passages

Search aliases: pmod

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Use in source · RESEARCH_NOTE.md, line 36
p^k+jL≡ p^kpmod M.
Exact mathematical passage
```
p^{k+jL}\equiv p^k\pmod M.
```

QUse in source · 2 passages

Search aliases: Q

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

qUse in source · 5 passages

Search aliases: q

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

q^kUse in source · 5 passages

Search aliases: q^k

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Use in source · RESEARCH_NOTE.md, line 24
e_k=q^k-λ p^k-F(p,p^kbmod M).
Exact mathematical passage
```
e_k=q^k-\lambda p^k-F(p,p^k\bmod M).
```

q^LUse in source · 1 passage

Search aliases: q^L

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Use in source · RESEARCH_NOTE.md, line 56
E≥fracq^k(q^L-1)(q^L-p^L)2(p^L+1).tag1
Exact mathematical passage
```
\boxed{E\ge\frac{q^k(q^L-1)(q^L-p^L)}{2(p^L+1)}.}\tag{1}
```

q^sUse in source · 1 passage

Search aliases: q^s

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Use in source · RESEARCH_NOTE.md, line 111
E_s,d,k^sharp= fracq^k(q^s-p^s)(q^s-1)^d+12^d+1(p^s+1).tag3
Exact mathematical passage
```
\boxed{ E_{s,d,k}^{\mathrm{sharp}}=
\frac{q^k(q^s-p^s)(q^s-1)^{d+1}}{2^{d+1}(p^s+1)}.}\tag{3}
```

RUse in source · 1 passage

Search aliases: R

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

rUse in source · 3 passages

Search aliases: r

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

r_0Use in source · 1 passage

Search aliases: r_0

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Use in source · RESEARCH_NOTE.md, line 50
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
Exact mathematical passage
```
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
```

r_1Use in source · 1 passage

Search aliases: r_1

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Use in source · RESEARCH_NOTE.md, line 50
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
Exact mathematical passage
```
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
```

r_2Use in source · 1 passage

Search aliases: r_2

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Use in source · RESEARCH_NOTE.md, line 50
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
Exact mathematical passage
```
ur_0-(u+1)r_1+r_2=B(v-1)(v-u).
```

r_jUse in source · 1 passage

Search aliases: r_j

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

r_{k+j}Use in source · 1 passage

Search aliases: r_k+j

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Use in source · RESEARCH_NOTE.md, line 92
max_0≤ j≤ d+1|r_k+j|≥ fracq^k|q-p||P(q)|∑_j=0^d+1|a_j|. tag2
Exact mathematical passage
```
\boxed{
\max_{0\le j\le d+1}|r_{k+j}|\ge
\frac{q^k|q-p||P(q)|}{\sum_{j=0}^{d+1}|a_j|}.
}\tag{2}
```

\operatorname{rad}Use in source · 1 passage

Search aliases: rad operatorname

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

sUse in source · 1 passage

Search aliases: s

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Use in source · RESEARCH_NOTE.md, line 111
E_s,d,k^sharp= fracq^k(q^s-p^s)(q^s-1)^d+12^d+1(p^s+1).tag3
Exact mathematical passage
```
\boxed{ E_{s,d,k}^{\mathrm{sharp}}=
\frac{q^k(q^s-p^s)(q^s-1)^{d+1}}{2^{d+1}(p^s+1)}.}\tag{3}
```

\mathrm{sharp}Use in source · 1 passage

Search aliases: sharp mathrm

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Use in source · RESEARCH_NOTE.md, line 111
E_s,d,k^sharp= fracq^k(q^s-p^s)(q^s-1)^d+12^d+1(p^s+1).tag3
Exact mathematical passage
```
\boxed{ E_{s,d,k}^{\mathrm{sharp}}=
\frac{q^k(q^s-p^s)(q^s-1)^{d+1}}{2^{d+1}(p^s+1)}.}\tag{3}
```

tUse in source · 4 passages

Search aliases: t

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Use in source · RESEARCH_NOTE.md, line 62
t=fracB(v-1)(v-u)2(u+1), λ=fracB(v-1)+2tA(u-1), κ=B-t-λ A.
Exact mathematical passage
```
t=\frac{B(v-1)(v-u)}{2(u+1)},\quad
\lambda=\frac{B(v-1)+2t}{A(u-1)},\quad
\kappa=B-t-\lambda A.
```

t_NUse in source · 3 passages

Search aliases: t_N

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

uUse in source · 3 passages

Search aliases: u

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

u^jUse in source · 1 passage

Search aliases: u^j

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

vUse in source · 3 passages

Search aliases: v

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

v^jUse in source · 1 passage

Search aliases: v^j

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

xUse in source · 4 passages

Search aliases: x

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

x^{p^{N-1}}Use in source · 1 passage

Search aliases: x^p^N-1

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Use in source · RESEARCH_NOTE.md, line 124
t_N(x)=x^p^N-1pmod p^N.
Exact mathematical passage
```
t_N(x)=x^{p^{N-1}}\pmod {p^N}.
```

yUse in source · 3 passages

Search aliases: y

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Use in source · RESEARCH_NOTE.md, line 130
C_p,N(x,y)=fract_N(x)+t_N(y)-t_N(x+y)p pmod p^N-1,
Exact mathematical passage
```
C_{p,N}(x,y)=\frac{t_N(x)+t_N(y)-t_N(x+y)}p \quad\pmod {p^{N-1}},
```

zUse in source · 2 passages

Search aliases: z

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

z^jUse in source · 1 passage

Search aliases: z^j

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

|Use in source · 1 passage

Search aliases: |

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Use in source · RESEARCH_NOTE.md, line 92
max_0≤ j≤ d+1|r_k+j|≥ fracq^k|q-p||P(q)|∑_j=0^d+1|a_j|. tag2
Exact mathematical passage
```
\boxed{
\max_{0\le j\le d+1}|r_{k+j}|\ge
\frac{q^k|q-p||P(q)|}{\sum_{j=0}^{d+1}|a_j|}.
}\tag{2}
```

\kappaUse in source · 2 passages

Search aliases: κ kappa

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Use in source · RESEARCH_NOTE.md, line 44
r_j=Bv^j-λ Au^j-κ, j=0,1,2.
Exact mathematical passage
```
r_j=Bv^j-\lambda Au^j-\kappa,\qquad j=0,1,2.
```

\lambdaUse in source · 4 passages

Search aliases: λ lambda

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Use in source · RESEARCH_NOTE.md, line 18
mathscr R(n)=λ n+F(rad(n), nbmod M),
Exact mathematical passage
```
\mathscr R(n)=\lambda n+F(\operatorname{rad}(n),\,n\bmod M),
```

\sumUse in source · 3 passages

Search aliases: ∑ sum

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

\sum_{i=0}^{p-1}Use in source · 1 passage

Search aliases: ∑_i=0^p-1 sum

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Use in source · RESEARCH_NOTE.md, line 150
∑_i=0^p-1 C_p,N(1,i)≡ 1pmodp^N-1
Exact mathematical passage
```
\boxed{\sum_{i=0}^{p-1} C_{p,N}(1,i)\equiv 1\pmod{p^{N-1}}}
```

\sum_{j=0}^{d+1}Use in source · 2 passages

Search aliases: ∑_j=0^d+1 sum

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Use in source · RESEARCH_NOTE.md, line 80
Q(z)=(z-p)P(z)=∑_j=0^d+1a_jz^j.
Exact mathematical passage
```
Q(z)=(z-p)P(z)=\sum_{j=0}^{d+1}a_jz^j.
```

\equivUse in source · 3 passages

Search aliases: ≡ equiv

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Use in source · RESEARCH_NOTE.md, line 36
p^k+jL≡ p^kpmod M.
Exact mathematical passage
```
p^{k+jL}\equiv p^k\pmod M.
```

\leUse in source · 1 passage

Search aliases: ≤ le

Link to this entry ·

Use in source · RESEARCH_NOTE.md, line 92
max_0≤ j≤ d+1|r_k+j|≥ fracq^k|q-p||P(q)|∑_j=0^d+1|a_j|. tag2
Exact mathematical passage
```
\boxed{
\max_{0\le j\le d+1}|r_{k+j}|\ge
\frac{q^k|q-p||P(q)|}{\sum_{j=0}^{d+1}|a_j|}.
}\tag{2}
```

\geUse in source · 2 passages

Search aliases: ≥ ge

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Use in source · RESEARCH_NOTE.md, line 56
E≥fracq^k(q^L-1)(q^L-p^L)2(p^L+1).tag1
Exact mathematical passage
```
\boxed{E\ge\frac{q^k(q^L-1)(q^L-p^L)}{2(p^L+1)}.}\tag{1}
```

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research/addmul-arithmetic-reconstruction/README.md · 0 mathematical passages
research/addmul-arithmetic-reconstruction/RESEARCH_NOTE.md · 16 mathematical passages