# 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, subtract, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(frac(one, Exp(two, one)), _two_pow_t)
sub_expr2 = Add(Neg(sub_expr1), one, Neg(e))
expr = Equals(Add(subtract(sub_expr1, two), sub_expr2), Add(sub_expr1, Neg(two), sub_expr2)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right)\right) =  \\ \left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2 + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right)\right) \end{array} \end{array}

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.()(2)('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: 10
operands: 5
4Operationoperator: 10
operands: 6
5ExprTuple7, 8
6ExprTuple19, 12, 8
7Operationoperator: 10
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple19, 12
10Literal
11ExprTuple13, 33, 14
12Operationoperator: 17
operand: 32
13Operationoperator: 17
operand: 19
14Operationoperator: 17
operand: 20
15ExprTuple32
16ExprTuple19
17Literal
18ExprTuple20
19Operationoperator: 21
operands: 22
20Variable
21Literal
22ExprTuple23, 24
23Operationoperator: 25
operands: 26
24Operationoperator: 30
operands: 27
25Literal
26ExprTuple33, 28
27ExprTuple32, 29
28Operationoperator: 30
operands: 31
29Literal
30Literal
31ExprTuple32, 33
32Literal
33Literal