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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 ExprRange, Variable, k, m
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))
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())
|\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}, \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)| = |\left(1, \ldots, 2\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10
8Operationoperator: 31
operands: 11
9Operationoperator: 31
operands: 12
10ExprRangelambda_map: 13
start_index: 14
end_index: 37
11ExprTuple16, 15
12ExprTuple16, 17
13Lambdaparameter: 22
body: 22
14Literal
15Operationoperator: 29
operands: 19
16Literal
17Operationoperator: 20
operand: 24
18ExprTuple22
19ExprTuple37, 33, 34, 23, 35
20Literal
21ExprTuple24
22Variable
23Literal
24Operationoperator: 25
operands: 26
25Literal
26ExprTuple27, 28
27Operationoperator: 29
operands: 30
28Operationoperator: 31
operands: 32
29Literal
30ExprTuple37, 33, 34, 35, 36
31Literal
32ExprTuple37, 38
33Literal
34Literal
35Variable
36Variable
37Literal
38Literal