logo

Expression of type Mult

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 k, m
from proveit.numbers import Exp, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))))
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())
\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}
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',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 18
operands: 1
1ExprTuple2, 3
2Operationoperator: 20
operands: 4
3Operationoperator: 20
operands: 5
4ExprTuple7, 6
5ExprTuple7, 8
6Operationoperator: 18
operands: 9
7Literal
8Operationoperator: 10
operand: 13
9ExprTuple26, 22, 23, 12, 24
10Literal
11ExprTuple13
12Literal
13Operationoperator: 14
operands: 15
14Literal
15ExprTuple16, 17
16Operationoperator: 18
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple26, 22, 23, 24, 25
20Literal
21ExprTuple26, 27
22Literal
23Literal
24Variable
25Variable
26Literal
27Literal