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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 Function, Variable, k
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _alpha_m, _m_domain, _phase, _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Equals(_alpha_m, Mult(frac(one, Exp(two, frac(_t, two))), Sum(index_or_indices = sub_expr1, summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Function(Variable("_a", latex_format = r"{_{-}a}"), sub_expr1)), domain = _m_domain)))
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_{m} = \left(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot {_{-}a}\left(k\right)\right)\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: 38
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Variable
9Operationoperator: 21
operands: 11
10Operationoperator: 12
operand: 15
11ExprTuple54, 14
12Literal
13ExprTuple15
14Operationoperator: 48
operands: 16
15Lambdaparameter: 45
body: 17
16ExprTuple52, 18
17Conditionalvalue: 19
condition: 20
18Operationoperator: 21
operands: 22
19Operationoperator: 38
operands: 23
20Operationoperator: 24
operands: 25
21Literal
22ExprTuple53, 52
23ExprTuple26, 27
24Literal
25ExprTuple45, 28
26Operationoperator: 48
operands: 29
27Operationoperator: 30
operand: 45
28Operationoperator: 32
operands: 33
29ExprTuple34, 35
30Variable
31ExprTuple45
32Literal
33ExprTuple36, 37
34Literal
35Operationoperator: 38
operands: 39
36Literal
37Operationoperator: 40
operands: 41
38Literal
39ExprTuple52, 42, 43, 44, 45
40Literal
41ExprTuple46, 47
42Literal
43Literal
44Literal
45Variable
46Operationoperator: 48
operands: 49
47Operationoperator: 50
operand: 54
48Literal
49ExprTuple52, 53
50Literal
51ExprTuple54
52Literal
53Literal
54Literal