# 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 e
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(e)
expr = Equals(Add(e, Add(Neg(_two_pow__t_minus_one), one, sub_expr1)), Add(e, Add(Neg(Mult(frac(one, Exp(two, one)), _two_pow_t)), one, sub_expr1)))

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(e + \left(-2^{t - 1} + 1 - e\right)\right) = \left(e + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 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: 26
operands: 5
4Operationoperator: 26
operands: 6
5ExprTuple19, 7
6ExprTuple19, 8
7Operationoperator: 26
operands: 9
8Operationoperator: 26
operands: 10
9ExprTuple11, 39, 13
10ExprTuple12, 39, 13
11Operationoperator: 34
operand: 17
12Operationoperator: 34
operand: 18
13Operationoperator: 34
operand: 19
14ExprTuple17
15ExprTuple18
16ExprTuple19
17Operationoperator: 36
operands: 20
18Operationoperator: 21
operands: 22
19Variable
20ExprTuple38, 23
21Literal
22ExprTuple24, 25
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 29
25Operationoperator: 36
operands: 30
26Literal
27ExprTuple33, 31
28Literal
29ExprTuple39, 32
30ExprTuple38, 33
31Operationoperator: 34
operand: 39
32Operationoperator: 36
operands: 37
33Literal
34Literal
35ExprTuple39
36Literal
37ExprTuple38, 39
38Literal
39Literal