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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import l
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _rel_indexed_alpha, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Equals(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\alpha_{b_{\textit{f}} \oplus l} = \left(\frac{1}{2^{t}} \cdot \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operand: 8
4Operationoperator: 43
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 52
operands: 13
10Operationoperator: 52
operands: 14
11Literal
12ExprTuple54, 55
13ExprTuple20, 56
14ExprTuple15, 16
15Operationoperator: 38
operands: 17
16Operationoperator: 38
operands: 18
17ExprTuple20, 19
18ExprTuple20, 21
19Operationoperator: 46
operand: 24
20Literal
21Operationoperator: 46
operand: 25
22ExprTuple24
23ExprTuple25
24Operationoperator: 57
operands: 26
25Operationoperator: 57
operands: 27
26ExprTuple29, 28
27ExprTuple29, 30
28Operationoperator: 43
operands: 31
29Literal
30Operationoperator: 43
operands: 32
31ExprTuple59, 34, 35, 33
32ExprTuple59, 34, 35, 36
33Operationoperator: 38
operands: 37
34Literal
35Literal
36Operationoperator: 38
operands: 39
37ExprTuple40, 41
38Literal
39ExprTuple48, 42
40Operationoperator: 43
operands: 44
41Operationoperator: 46
operand: 55
42Operationoperator: 46
operand: 49
43Literal
44ExprTuple56, 48
45ExprTuple55
46Literal
47ExprTuple49
48Operationoperator: 50
operand: 54
49Operationoperator: 52
operands: 53
50Literal
51ExprTuple54
52Literal
53ExprTuple55, 56
54Literal
55Variable
56Operationoperator: 57
operands: 58
57Literal
58ExprTuple59, 60
59Literal
60Literal