# 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.
# import Expression classes needed to build the expression
from proveit import e
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions

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(\left(2^{t - 1} - 2\right) + \left(-2^{t - 1} + 1 - e\right)\right) = \left(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-2^{t - 1} + 1 - e\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: 34
operands: 5
4Operationoperator: 34
operands: 6
5ExprTuple7, 9
6ExprTuple8, 9
7Operationoperator: 34
operands: 10
8Operationoperator: 34
operands: 11
9Operationoperator: 34
operands: 12
10ExprTuple24, 14
11ExprTuple13, 14
12ExprTuple15, 41, 16
13Operationoperator: 17
operands: 18
14Operationoperator: 39
operand: 36
15Operationoperator: 39
operand: 24
16Operationoperator: 39
operand: 25
17Literal
18ExprTuple22, 23
19ExprTuple36
20ExprTuple24
21ExprTuple25
22Operationoperator: 26
operands: 27
23Operationoperator: 32
operands: 28
24Operationoperator: 32
operands: 29
25Variable
26Literal
27ExprTuple41, 30
28ExprTuple36, 37
29ExprTuple36, 31
30Operationoperator: 32
operands: 33
31Operationoperator: 34
operands: 35
32Literal
33ExprTuple36, 41
34Literal
35ExprTuple37, 38
36Literal
37Literal
38Operationoperator: 39
operand: 41
39Literal
40ExprTuple41
41Literal